A woman jailed for murdering her 18-month-old daughter can now be named after abandoning her bid for continued name suppression.

Southern Thompson was sentenced in May for abusing, neglecting and bashing Comfort Jay Thompson-Pene to death in their Tirau home in July 2018.

She was jailed for life with a minimum non-parole period of 17 years on charges of murder, ill-treatment of a child, injuring her with intent and failing to seek medical care.

"Your offending involved systematic abuse of a young child who was defenceless," Justice Graham Lang said in the High Court at Rotorua on May 13.

Her lawyer filed a last-minute application for name suppression during the hearing. The application was dismissed by Justice Lang, but that decision was immediately challenged, requiring suppression to remain in force until the appeal is heard.

Media, including Open Justice, challenged the suppression appeal.

Today, Thompson gave formal notice to the Court of Appeal that she was abandoning her appeal, meaning suppression of her name lapses.

The offending

Comfort Jay Thompson-Pene was born with a birth defect, and she spent the first few months of her life in hospital.

She was discharged from the hospital healthy, but was vulnerable and needed extra care.

A police summary of facts, released to Open Justice, said Thompson approached a neighbour asking to use their phone on July 23, 2018, because her daughter was unwell.

She called Healthline and said the child was non-responsive. Healthline staff repeatedly urged her to call an ambulance and offered to call one for her.

Despite being told her daughter urgently needed to see a doctor in the next hour, she said she couldn't take her due to other matters.

She ended the call to Healthline, and two hours later called 111 for an ambulance.

Ambulance staff arrived and found the child lying on her back on the floor. She wasn't moving, and they initially thought she was dead.

The staff described the mother as being "detached", and more interested in returning the phone she had borrowed than in how seriously ill her daughter was.

Ambulance staff noticed the child was only dressed in a small skivvy, and was so cold they were unable to get a body temperature reading.

A rescue helicopter was called and took the child to hospital where she was put on life support. It was found she had suffered irreversible brain injuries that were not survivable.

Her life support was switched off at 10am on July 24, 2018.

The summary of facts described the fatal injuries as well as the ill-treatment and abuse suffered by the child in the months leading up to her death.

An autopsy concluded she died as the result of head injuries due to blunt force trauma. There had been a number of impacts to the head, which led to a blood clot over the surface of the brain as well as bleeding over the surface of the brain.

The injuries caused the brain to swell, and ultimately for the child to die.

She also had extensive bruising around her head, some of which were fresh injuries. Others were older.

The summary said it was difficult to be precise about the timing of when the fatal injuries were caused, but chemicals found in slides taken from the child's brain indicated the fatal injuries were likely to have been inflicted late on Saturday 21 July, or sometime during the following Sunday.

Her condition would have been significantly deteriorating over the hours from the infliction of the injury until she was taken to hospital.

It was still not known how the injuries were caused as no explanation was provided.

The mother said she assaulted her child by pushing her in the chest on the day she finally sought medical attention, but denied any assaults to her head.

The only explanation given was the child had fallen down two concrete stairs on Saturday afternoon landing on her shoulder.

The summary said the mother would hit her daughter on a regular basis, and the child was seen by a number of people with two black eyes and a cut lip.

There was extensive soft tissue bruising to her body not consistent with accidental injuries.

Doctors found her body covered in healing scratch marks, especially around her neck and chest. She also had extensive bruising on her body consistent with excessive application of fingertip-force from adult-sized hands.

A police investigation found that before her death she was subjected to ongoing neglect and physical abuse.

Her body was malnourished and she weighted only 8 kilograms, placing her in the second percentile, or lighter than 98 per cent of girls the same age.

She was in the 50th percentile when she was last weighed by a nurse in July 2017.

The summary said the only medical explanation was that she was not being fed enough.

The child was confined to her room for hours. During the winter months the family all slept in the lounge, due the cold nature of the house.

When they moved into the lounge, the child was given a corner of a couch and confined there for hours. If she got off or moved, she would be assaulted by her mother.

At the time of her death, she had "severe and extreme" nappy rash. It was so extensive she had large areas of skin peeling from parts of her buttocks.

This represented chronic neglect of basic care, the summary said.

It was further noted that the child had chronic rubbing injuries around where the nappy elastic sat, indicating she spent long periods in wet nappies.

The child also had a large ulcer under her chin, most likely caused by her dribbling. No effort was sought to treat it and at the time of her death it was large and raw. Regular bathing and cleaning would have properly dealt with the issue, the summary said.

The family home was described as being in a "dreadful state". It was so dirty, police found a mouldy bowl of noodles left on the kitchen bench which had maggots in it.

It was cold, damp, had broken windows, and no lightbulbs worked. There was old and rotting food on the floor, dirty nappies lying around in the living area where occupants of the house slept on a mattress, and dirty clothes and rubbish throughout. Cannabis and alcohol cans were also found.

The summary said the child was found with a torn frenula injury, which is generally caused as a result of forcible impact, such as from a blow to the face.

Experts considered it to be from significant or repeated force. She had also suffered the loss of a front tooth, and a tooth next to the missing tooth was loose.

A post-mortem report said the dental injuries were likely caused from significant blunt force trauma about two weeks before the child's death.

The mother admitted she would assault her child to the face and mouth area, causing her "fat lips" and a bleeding mouth.

She also had a healing fracture to her left clavicle, or collarbone, that was a number of weeks old. The cause of the fracture was unknown.

The summary said regardless of the cause, it was a significant break that was clearly visible to the naked eye, due to one of the bones protruding just below the skin, and there was no doubt it would have been immediately noticeable to the mother on a daily basis.

The child would have been in significant pain and would have had difficulty manoeuvring her arm. At no stage did the mother seek any medical care for the child for this broken bone.