A man accused of murdering his 2-year-old stepdaughter hated the toddler looking like her father and said she should go and live with him, the girl's mother has told his trial.

Michael Joseph Martin, 25, is on trial in the High Court at Auckland over the death of Leilani Mary-Jane Lotonu'u at their Manurewa property on June 9, 2012.

The Crown says he hit her in the stomach hard enough to split an organ and a resulting infection proved fatal.

The defence says Leilani's mother, Amy Lorigan, 21, must have been responsible. She has denied that.

Ms Lorigan and Martin had been together since early 2011 and also had a child of their own. But after Ms Lorigan fell pregnant to him, their relationship changed, she told the court today.

On one occasion Ms Lorigan came home to find Martin had put all hers and Leilani's belongings in the garage.

Martin told Ms Lorigan to "f... off".

He later blamed his behaviour on alcohol and said sorry.

Another time, the pair briefly broke up after Martin said: "I hate the fact that Leilani looks like her father".

Later he told Ms Lorigan Leilani should live with her dad and that she cried too much.

"He said it made him angry frustrated that she was a sook because she would cry," Ms Lorigan said.

She told the court about returning home one day in June, 2012 to find vomit on the floor. Martin told her Leilani had fallen off a chair, thrown up and started crying.

The Crown says Martin later offered this explanation to police about Leilani's fatal injuries and after her death, a medical examination revealed the existence of an earlier injury.

Several witnesses have described Ms Lorigan's and Martin's house as dirty and smelly. Ms Lorigan said she didn't think it was at the time, but she had since changed her view.

Martin has also pleaded not guilty to a charge of child neglect for failing to provide Leilani with medical assistance.

This afternoon the court heard details of Leilani's last days.

Ms Lorigan spoke about picking Leilani and her younger daughter up from her mother's house on June 7. The girls had been at her mother's house for six days.

"I was happy, I was excited," she said.

Both girls appeared happy to see their mother.

They were dropped home, and after not seeing her kids for so long, Ms Lorigan wanted to spend time with them.

"I just wanted to watch movies and spoil them. I bought Leilani food that she liked to eat and let her choose her own lollies and fizzy drinks," she told the court.

Martin arrived home later and the family all slept in the lounge.

Ms Lorigan said Leilani was "fine" and woke up once in the night. She changed the toddler's nappy and gave her some chips to eat, then she went back to bed.

The next day, June 8, Leilani was still "fine". She had breakfast, played with her toys "as normal" and had an afternoon sleep.

Later in the afternoon Leilani sat at the table with her mother and Martin and looked at a book she used at preschool.

"We were both talking to her about her book, looking through the book," she said.

"I told her that I love her and she told me that she loved me too. She goes 'I love you Mikey' and [Martin] said 'I love you too Leilani'."

The family ate dinner before watching television and going to bed.

Ms Lorigan said there was nothing noticeably wrong with Leilani after she picked the girls up from her mother's, apart from nappy rash.

"She was fine," she said repeatedly in court.

The Crown is expected to continue questioning Ms Lorigan about Leilani's last days and her death tomorrow.