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Aaron Archer, 30, is accused of killing 2-year-old Ariah Dawn Roberts at Mangawhai on August 22, 2018 while her mother was at the supermarket buying dinner.
He allegedly inflicted "catastrophic" and "multiple" head injuries to the child within 15 minutes of her mother leaving the house.
The fatal injuries were compared to the child being involved in a serious car crash or falling at least two storeys.
Archer concedes he caused the death of the child, but denies a charge of murder, saying there was no intent, violence or abuse.
Until yesterday the little girl's name and her relationship to Archer could not be reported.
But Justice Christian Whata allowed media to report that she was Ariah Dawn Roberts.
Archer was in a relationship with her mother - whose name is suppressed - at the time of the alleged murder.
His trial in the High Court at Auckland started yesterday with a jury being selected.
Today the Crown opened its case against Archer.
It alleges that at 7.15pm on the day she died Ariah was left in Archer's care while her mother went to the supermarket.
She had no injuries at the time except an "old bruise" to her eye.
Fifteen minutes after her mother left, Ariah was not breathing - she had died.
Ariah died as a result of "multiple blows or blunt force trauma to the head".
She had at least 20 bruises to her head and face - one of the impacts causing the fatal injuries
The court was told her injuries were equivalent to a road traffic accident or falling from a height of at least two storeys.
She suffered a "massive brain injury" and her head and face were covered in bruises.
There were even bruises behind her ears and on her tummy.
"Ariah was not injured in that manner when her mother left… so therefore we do know when these injuries occurred and it was when she was in the sole custody of Aaron Archer," said Crown prosecutor Olivia Klaassen.
An expert told the Crown that catastrophic injuries did not occur from the usual tumbles and falls of a toddler.
If they did occur they were usually associated with "significant trauma" such as serious car crashes or falling.
"Aaron Archer caused these injuries… he was the only one home with Ariah, he acknowledged this to attending paramedics," Klaassen told the court in her opening address.
"He told Ariah's mother he was swinging her around and she hit her head…. Along with other explanations that he dropped Ariah… or that he threw her up and she slipped.
"The key evidence is that… these injuries do not marry up with the defendant's explanation of what occurred."
The jury will hear evidence from medical experts, specialist scene examination staff and first responders who attended the initial 111 call and tried to revive Ariah before she was pronounced dead at the scene.
They will also hear from neighbours as to what they saw or heard on the day.
Ariah's mother, who went to the supermarket to get dinner when her child was killed, will tell the jury her side of the story - including how Archer left her a voicemail message while she was out.
She will give evidence that Ariah was not injured when she left the house that fateful night.
Expert pathologists will also be called by the Crown and will explain how Ariah's injuries were "abusive".
Klaassen said Archer admitted at the scene that he had caused the child's injuries but claimed it was an accident.
He refused to speak to police when later taken to the Wellsford station - which is his right.
Members of both Ariah's and her alleged killer's families were in court today.
Her mother was not present, and like other witnesses, cannot attend the trial until after she has given evidence.
It is understood little Ariah was a twin, but her brother tragically died at birth.
Klaassen said it was "clear cut" that Archer was lying and his multiple explanations about what happened to Ariah "just do not stack up".
"Someone is lying," she said.
"And it's not the experts.
"The defendant was clearly reckless about whether his violence would be fatal... we can infer that there is an intent to cause real harm."
Klaassen told the jury that the evidence they would hear would not be pleasant and would include images of Ariah's body post mortem.
Defence lawyer Annabel Maxwell-Scott, standing in for Ron Mansfield, said her client did not murder Ariah.
"There is nothing sadder than the death of a child," she said.
"The defence case is simple, it was an awful tragic accident - and it was an accident."
She said the recording of Archer's phone call to his then-partner would be played and the jury would hear from people at the scene who spoke to the distraught stepfather.
She said his reaction was "consistent" with a terrible accident befalling Ariah.
"He did not intend to kill Ariah, did not intend to assault her - this was a tragic accident," said Maxwell-Scott.
The trial continues.