Judge Russell Callander imposed a variety of suppression orders but allowed the publication of a summary of facts, which said Ms Aim died after receiving two heavy blows in rapid succession to the left side of the head and then a further heavy blow to her face.
The summary said these blows caused extensive fractures to her skull and a pathologist had concluded she died from the trauma to her head.
Ms Aim was on a working holiday in Taupo and was killed while walking back to her flat after a night of socialising with friends.
She was found lying critically injured on a street corner by a police officer who had been called to investigate vandalism at Taupo Nui-A-Tia College. She was near the college and less than 100m from her flat, and died a short time later in Taupo Hospital.
Fletcher Pilditch, lawyer for the police, told the court Ms Aim was surrounded by "a significant amount of blood" when the constable spotted her in the early hours of January 17.
"Her skirt had been lifted up and her underpants torn or ripped," he said. "Her wallet was found lying on her stomach."
He said Ms Aim was making a noise but was unresponsive, and an ambulance was called.
Police allege that the accused was also responsible for the vandalism at the college, smashing 19 windows and causing $5300 of damage with the same baseball bat he used to kill Ms Aim a few minutes later.
Security footage showed a person riding a distinctive bicycle in the school grounds between 2.04am and 2.10am. Ms Aim was found at 2.32am.
When the accused was put under surveillance two days after the murder, he was seen riding the same bicycle, and after four days of watching him, police executed a search warrant on his house.
There they found Ms Aim's digital camera. Forensic analysis of the memory stick revealed photos of her and her friends travelling around New Zealand, despite the images having been deleted.
New photos of a young child linked to the accused were on the camera, the first taken on the afternoon of January 17, Mr Pilditch said.
Ms Aim's handbag was also found in an incinerator at the back of the house and a baseball bat with glass embedded in it was found under the building.
DNA analysis revealed the blood belonged to Ms Aim.
Five members of the accused's family and a Child, Youth and Family supervisor were in court yesterday.
Police plan to present evidence from 102 witnesses during the remainder of the hearing.