'My heart just sank.' William Tyrrell's foster mother recalls the morning he disappeared, & more in News in 5.

— With AAP.

1. Coroner hears from William Tyrrell’s tearful foster mother during inquest.

William Tyrrell’s foster mother has cried while telling a NSW coroner of the moment she recalled seeing two cars parked on a nearby road the morning he disappeared.

“My heart just sank because I just thought those two cars were there for both of them,” she said on Monday, referring to the three-year-old boy and his sister.

The woman told day one of the Sydney inquest into William’s disappearance and suspected death she recalled the white and gunmetal grey vehicles with tinted windows in the days after he went missing in September 2014.

The family had been visiting his foster grandmother’s house in Kendall on the NSW mid north coast.

Counsel assisting the coroner, Gerard Craddock SC, asked why the cars weren’t mentioned in her original statement.

“I didn’t even think about it because I saw the cars, walked back inside and got swept up in the emotions of getting everybody ready for the day and then with William missing it went right out of my brain,” she replied.

The woman also wept when she recalled seeing a third vehicle that morning – a green or teal-looking car which reversed in a neighbouring driveway and drove off.

She said the driver was “a big man” in his late 50s who was Caucasian, had “sandy, reddy-coloured hair”, a “thick neck” and looked “weathered”.

They exchanged a fleeting “Why are you watching me? I’m watching you” glance, she said.

The foster mother said she was still working with police to reconstruct the man’s appearance with software but had a “pretty intense reaction” when she identified the “old” green car.

“I can’t tell you how much I rack my brain and I beat myself up over not looking at number plates,” she said.

She also recalled the exact moment when William went missing while playing “daddy tiger” and running out of sight.

“I hear a roar and then I hear nothing,” she told the court.

She raced around the property, looking in every cupboard and every bush for a sign of his red Spiderman suit.

“William, it’s Mummy. You need to tell me where you are. You need to say something,” the woman recalled through tears.

“He was gone.”

In his opening address, Mr Craddock said he expected the evidence before the inquest would show it was likely the boy was taken.

“That is, that William’s disappearance was the direct result of human intervention,” he said.

“If the evidence establishes William was abducted, that conclusion is chilling because it means a person snatched a three-year-old from the safety of a quiet village backyard.”

In a police video aired in court, taken in a backyard six days after William vanished on September 12, his foster father tells an officer: “He never wanders. He’s not a wanderer.”

The first week of hearings will explore William’s foster and biological families, when he disappeared and the action taken shortly after he went missing.

Mr Craddock said there was no doubt William’s biological parents were in Sydney the day he disappeared.

“Investigators haven’t positively drawn the conclusion that no relative or associate was involved in William’s disappearance,” he said.

Further hearings, also before Deputy State Coroner Harriet Grahame, will be held in August when persons of interest will be called to testify.

“I acknowledge at the outset, to have a child go missing must be one of the greatest pains a human can experience,” she said on Monday.

Listen to The Quicky debrief on the truth about William Tyrrell’s parents, and what happened after the three-year-old’s disappearance. Post continues below.

2. Gladys Berejiklian wins majority in NSW parliament.

NSW Labor's woes are continuing with uncertainty over the party's leadership to go on for months in the middle of a federal election while the coalition has won a majority in the NSW parliament.

Michael Daley on Monday evening quit as Labor leader following the party's poor showing in the weekend's state election, but says he intends to re-nominate after the federal poll.

Mr Daley said he would stand aside until after the federal election - due in May - with deputy leader Penny Sharpe to fill in as interim leader.

The Berejiklian government secured a majority in NSW by winning 48 seats in the 93-seat lower house.

On Monday evening the ABC called the electorate of East Hills as being retained by the Liberals.

Mr Daley said he would stand aside until after the federal election - due in May - with deputy leader Penny Sharpe to fill in as interim leader.

To do otherwise would be an unnecessary distraction from the task of trying to elect a Bill Shorten federal government, he said in a statement.

NSW Labor executives delayed the leadership spill until after the federal election to limit any negative impact on the federal campaign.

Mr Daley told reporters he intends to re-nominate for the leadership when nominations open.

A ballot is required following an election defeat under the party's rule. The ballot is of the caucus and rank-and-file members with both blocks given equal weight.

Mr Daley said under normal circumstances an interim leader would be appointed until a ballot was called, and while the process had been interrupted by the impending federal election, it was in the spirit of the rules for him to stand down.

His final week of the campaign involved two major blunders.

A video from September emerged of the-then Opposition telling a pub forum that Asian migrants were taking local jobs and he then stumbled on key numbers behind his education policies during a live television debate.

However, Mr Daley has defended his record saying he had "picked up the pieces that the party was in" when he took over in November following the resignation of Luke Foley.

He denied the decision to renominate for the leadership could hurt federal Labor, saying standing aside as leader "removes the distraction".

Interim leader Ms Sharpe suggested the new full-time leader would be in place by the end of June.

Kogarah MP Chris Minns is touted as a top contender with Labor frontbencher Jodi McKay also a possible challenger.

3. Jacinda Ardern announces royal commission into whether Christchurch shooting could have been prevented.

New Zealand's government says no stone will be left unturned during a royal commission into whether authorities could have stopped the Christchurch terror attack that killed 50 people.

Since the mosque shootings on March 15, questions have been asked about how the lone man charged, 28-year-old Australian white supremacist Brenton Tarrant, was not flagged by security agencies on either side of the Tasman.

While New Zealand's government last week promised a probe would be held, Ardern on Monday confirmed it would be a royal commission - the most serious form of investigation possible into failures of government.

"In short, the inquiry will look at what could have and should have been done to prevent the attack. It will inquire into the individual and his activities before the terrorist attack," she told reporters in Wellington.

"While New Zealanders and Muslim communities around the world are both grieving and showing compassion, they are also quite rightly asking about how this terror attack was able to happen here."

Intelligence agencies, police, customs and the immigration department will be subject to investigation.

While the minister in charge of New Zealand intelligence, Andrew Little, has said increased attention had been paid to the alt-right and white supremacy in recent months, Ardern told media the commission would ask whether resources had been put in the right place.

"I want recommendations on how any such attack in the future could be stopped," she said.

Separately, her government is also turning its attention to social media companies.

A live-stream of the shooting continues to circulate online despite authorities social media companies like Facebook working to have it taken down. Facebook said it pulled down the video 1.5 million times in the first day after the attack.

"My question generally, across all of these platforms, is what can we put in place or have assurances around to ensure this doesn't happen again," Ardern said.

"We are as a cabinet having a conversation around meaningful change in the area of social media."

Several people are already being prosecuted for distributing the now-banned video in New Zealand and face up to 14 years' jail.

New Zealand's chief censor has also put a similar ban on a rambling 74-page "manifesto" posted by the gunman, spurring debate about free speech.

Tarrant - who will appear in court again next week on what is expected to be a raft of charges - is known to have participated on internet forums populated by right-wing extremists and foreshadowed the attack online, before live-streaming it using a helmet camera.

In Australia, South Australian senator Rex Patrick has called for a wide-ranging inquiry into far-right extremism following the attack.

"There is in fact a real dearth of hard information and analysis on right-wing extremist violence in Australia," he said on Monday.

Prime Minister Scott Morrison and opposition leader Bill Shorten will discuss the issue of violent online content with representatives from social media giants in Brisbane on Tuesday.

A New Zealand national memorial service has been announced for Friday.

4. Snowtown serial killer claims there's "no point" in apologising for murders.

Snowtown serial killer Robert Joe Wagner says "there's no point" showing remorse for the murders of 10 people because any apology he makes would not be taken seriously.

Wagner, 47, represented himself before the South Australian Supreme Court on Monday in his bid to have a non-parole period set on his life sentence.

Relatives of his victims are opposed to any possible release, fearing he may kill again.

After Wagner listed cases where a non-parole period has been granted, including that of Truro killer James Miller, Justice Greg Parker asked him "you're not suggesting that you've shown contrition, remorse?"

Wagner said any suggestion of remorse would be dismissed as disingenuous.

"So there's no point in me saying I'm sorry or I feel remorse for what I've done," he said from the dock.

Since 1999, Wagner has been serving 10 life sentences over the infamous "bodies-in-the-barrels" killing spree.

The ringleader in the murders, John Justin Bunting, is similarly serving life without parole.

South Australian victims' rights commissioner Bronwyn Killmier told the court Wagner's application was "a slap in the face" for families affected.

"The prisoner has stated that the setting of a non-parole period would assist his mental wellbeing, but it would not help the mental wellbeing of the people suffering because of his actions," lawyer Noah Redmond told the court, as Ms Killmier sat in the gallery

"It is, in fact, abhorrent to them that he might be given an opportunity to be released."

Mr Redmond said the victims had suffered lasting effects as a result of Wagner's crimes, and take some comfort knowing he will never be released.

"They do not believe that Wagner has reformed, rehabilitated or demonstrated remorse," he said.

"In fact, a number of the victims believe that he is not finished and if released, he will kill again."

Prosecutor Carmen Matteo said Wagner's crimes were "of unparalleled seriousness" and urged Justice Parker to dismiss the application.

The serial killings were exposed in 1999 when police found eight dismembered bodies in acid-filled barrels in the vault of a disused bank at Snowtown, north of Adelaide.

Two more bodies were found buried in a backyard at suburban Salisbury North while detectives later linked two further deaths to Bunting and Wagner.

After a trial lasting 170 days, Bunting was found guilty of 11 murders with Wagner jailed over 10 of the deaths.

Two other men, Mark Ray Haydon and James Spyridon Vlassakis, are also behind bars over the killings; Vlassakis after pleading guilty to four murders and Haydon for helping Wagner and Bunting dispose of the bodies.

Justice Parker reserved his decision until a date to be set.

5. The national ban on mosque shooter's manifesto questioned by New Zealand free speech advocates.

New Zealand free speech advocates are questioning a national ban on the Christchurch mosque shooter's rambling "manifesto", saying it goes too far and will hinder debate about the causes of extremism.

The country's chief censor over the weekend issued a decision that means having any copies of the 74-page document, written by 28-year-old Australian white supremacist Brenton Tarrant, is illegal and distributing it could lead to as much as 14 years' jail.

Several people have already been charged with distributing a separate live stream of the March 15 terror attack in which 50 were killed.

But while it doesn't question a ban on that footage, New Zealand's Free Speech Coalition says censorship of the text goes too far.

"Most New Zealanders will have no interest in reading the rants of an evil person," constitutional lawyer and coalition spokesman Stephen Franks said.

"But there is a major debate going on right now on the causes of extremism ... New Zealanders need to be able to understand the nature of evil and how it expresses itself."

He said documents such as Adolf Hitler's Mein Kampf were still on sale and citizens needed to be able to "engage, hear, read, and reject evil for themselves".

But Chief Censor David Shanks said the document was more closely in line with ISIS propaganda - which is also banned - and crossed the line beyond hate speech that could be considered troubling but legal.

"It identifies specific places for potential attack in New Zealand, and refers to the means by which other types of attack may be carried out," he said.

"It contains justifications for acts of tremendous cruelty, such as the deliberate killing of children."

Shanks wouldn't call the document a manifesto, instead describing it as a "crude booklet that promotes murder and terrorism".

Asked about the ban, Prime Minister Jacinda Ardern on Monday said it was up to the censor, but she personally felt it was the right decision.

Under the law, reporters and academics are allowed to apply for special exemptions to hold copies of the document.

The debate comes as New Zealand media organisations grapple with how to cover Tarrant and his upcoming legal case. With the NSW-raised man reportedly planning to represent himself, there are fears he will use the trial process as a platform for extremist rhetoric.

New Zealand Prime Minister Jacinda Ardern last week said she would not be using the gunman's name in a bid to deny him the notoriety he was seeking. The country's two biggest news organisations have taken up the call by keeping mentions by name to a minimum.