The many lines of inquiry investigated in the William Tyrrell mystery have all failed to lead police to his captor.

But each has fanned the feverish public intrigue in what happened to the little boy in the Spider-Man suit, making it Australia’s most perplexing unsolved crime.

The three-year-old disappeared while he played outside his foster grandmother’s home on Benaroon Dr, Kendall on the morning of September 12, 2014.

The property is at the end of a quiet cul-de-sac, prompting doubts William’s kidnapper happened upon him by chance.

William only arrived at the home the previous evening, on an impromptu visit with his foster family.

He had been playing with his sister in the yard while his mother and grandmother watched.

They were inside for a moment but could hear William’s playful giggles. Then the sounds stopped.

“My son’s missing, he’s 3½,” his mother said in a triple-0 call.

“We heard him then we heard nothing ... He’d be about 2½ foot. He’s wearing a Spider-Man outfit.”

For the next 10 hours more than 100 police and volunteers scoured 18sqkm for a little boy they believed was lost.

They found no trace of him. But the nation had already seen a photo of a gorgeous smiling boy, wearing a Spider-Man suit, playing in his home and fallen in desperate wonder with his story.

Journalists went digging to discover William’s family situation but met legal barriers preventing them from publishing it for years.

William was a foster child. He was taken from his biological parents Karlie Tyrrell and Brendan Collins at eight months old and placed in the care of a family on Sydney’s north shore.

He was with his foster family when he went missing.

In August 2017, a Supreme Court judge ruled the matter was of “legitimate public interest” and allowed the details of his care to be reported. So followed the gradual surfacing of William’s biological family in media reports and tell-all TV interviews.

Perhaps most stunning though, were Collins’ comments this week, his first since William vanished.

“I’m so sorry for whoever’s done this to you William, I don’t know who took you in your Spider-Man suit,” Mr Collins said.

“I’ve been out looking for you with a shovel digging in bushland … I know there’s no point.

“I think you’re dead, I think someone has hurt you bad. I’m so sorry I couldn’t help you.

“I tried to run away with William when he was nine months, we were happy, just me and him for seven weeks, until DOCs took him into care.

“I know I’ve had a history of drugs problems but I’d never harm my boy.

“DOCS took him from me to keep him safe and now … he’s probably dead.”

William’s biological grandmother Natalie Collins then declared she had given up hope of finding him, denouncing the massive fresh search launched by police this week as a waste of time.

“This is just opening old wounds for us, the door never closes, the police are wasting good taxpayers’ money and their time, they’re never going to find William — I just know in my heart he’s dead,” she said.

“I know exactly what’s happened, someone’s taken him and done something to him. Brendan says it, too, he believes William’s gone.

“What clues are they looking for? William can’t even walk that far to Kendall, he’s not there.”

Karlie Tyrrell opened up during a television interview in February, saying she felt like the “worst mum in the world”.

William’s foster parents have spoken sparingly to the media, and have done so in co-operation with investigators. They have vowed never to give up searching for him.

“Hearts across Australia have been broken, but we have and will continue to maintain unwavering faith in NSW Police and carry hope in our hearts that William will be found. He is in our hearts always … Always…,” they wrote this week via the Facebook page Where’s William Tyrrell? — Bring Him Home.

In the weeks after William vanished, investigators turned their attention to a handyman William Spedding who quoted on a washing machine repair for William’s grandmother before the disappearance.

Officers scoured his home, raided a business and even pumped out his septic tank.

Nothing was found and he was never charged

In September 2015, police announced they were looking for the drivers of two cars William’s mother had seen parked in the street that day — a white station wagon and an older-style grey sedan.

About the same time, the investigation reached a line of inquiry many feared it would.

Strike Force Rosann, set up to solve William’s case, was investigating a paedophile ring that had links to a mid-north coast social group called Grandparents As Parents Again (GAPA). Two GAPA members had been charged with indecently assaulting children in the year after William’s disappearance.

But Rosann boss, Homicide Squad’s Detective Chief Inspector Gary Jubelin, announced this week no new leads came from the group.

Jubelin faced a sea of cameras on Wednesday to announce more than 50 Public Order and Riot Squad officers would meticulously search 3sqkm around Benaroon Dr.

Despite being more than 3½ years since William was last seen in the area, police want one last sweep of the dense undergrowth to be certain he is not there.

If the search yields nothing, the case would likely be referred to a coronial inquest.

But Jubelin used the massive media pack that arrived to cover the search, to send a message to those who may have information about William’s disappearance.

“I dare say that with the intense interest in William’s disappearance that someone watching this now might be feeling very uncomfortable ... I’d suggest you come to us before we come to you,” Jubelin said.

“I strongly believe there are people out there who have information on this. If you do have information concerning what happened to William, you are at risk of committing a criminal offence by concealing an offence.”

Attention like that, according to leading forensic psychologist Dr Julian Parmegiani, could crush the resolve of someone holding on to critical evidence to protect themselves or a loved one.

“The more a crime is publicised or the demand for that information is made, the louder the conscience becomes to the point where it just becomes difficult to live with yourself,” Parmegiani says.

“There’s an internal struggle between your conscience and competing factors like allegiances to the perpetrator.

“It’s always in your face, you can’t use denial and say, ‘well someone else has got to come forward, it’s not my business, it’s not my role, it’s not my job to solve this crime. It’s not my role to betray my brother, husband, father, whoever.’ ”

Parmegiani believes that in the case of decent people “if the human face is right in front of you, day in, day out, sooner or later your conscience will make you do the right thing.”

If the person who knows the truth in William’s case is a sadistic criminal, however, the chances of a victory of conscience is unsurprisingly reduced.

“Something that’s taken such a degree of planning was probably preceded by a long period of fantasising about it ... They would probably go to the grave with their secret,” Parmegiani says.

“We’re more relying on people who are not habitual criminals and not psychopathic killers to come forward.

“The perpetrators usually don’t but someone close to them does.” He said higher-level offenders were, however, prone to boasting about their crimes.

Kendall resident Theo Hazlegrove said life there has changed forever.

“Kids used to play in the street, you would just drive slowly and everyone would respect that.

“Not any more,” he says.

CRIMINAL PROFILER: ABDUCTION WAS PLANNED

By Dr Xanthe Mallett, senior lecturer in criminology at the University of Newcastle.

If you look at the area William Tyrrell was taken from, it’s not where a child predator would hang out on the off-chance of finding a vulnerable victim to abduct.

It was clearly a targeted incident. It wasn’t what we call “situational”.

It is someone who has seen him or knows him. (Both his foster family and biological family have been cleared of any involvement).

What struck me immediately is that we’re not looking for the opportunistic predator that is going to hang around outside a school or a shopping centre, that’s looking to prey on any child that’s vulnerable.

It’s not that kind of offender at all.

It’s someone who went there specifically for William, whether that’s someone in the local community or who knows him from somewhere else.

They would have planned this in advance and waited for the opportunity when the carer’s back was turned.

The police have got a number of persons of interest, but to get on that list I think a pretty low bar has been set. They’re looking at everyone carefully. They will be looking at everyone he had any kind of contact with in the weeks leading up to his disappearance.

Are we looking at a sexual offender or someone who had another reason for abducting him?

Clearly the police have got some information that has led them back to the scene at this time.

They’re not sharing that, but they’re hopeful of finding something. It doesn’t fit the geography of where a sexual predator would normally go to target vulnerable children.

They certainly would have looked to the foster family first. The persons to last see someone alive are always the first to be investigated, but it’s a bit more complicated because you’ve got the foster family and the biological family — who the police have ruled out.

I think if he was abducted by a predator they’d take him further away than the 4km radius the police are looking in, but obviously they’ve got a reason for searching that area.