Key Points:

The Family Court is expected to hear arguments today about which parent a seven-year-old girl at the centre of a trans-Tasman custody row should live with.

Terry Thorne, who lives in Australia, and Nicola Richards will put forward arguments about why they should be awarded custody of Caitlin Thorne.

Mr Thorne said he moved to Australia 10 months ago to keep Caitlin away from her mother, who he said was a drug addict and in a relationship with an accused criminal.

Richards was bailed after appearing in court last week on drugs charges.

Her boyfriend Iain Clegg is in custody charged with the murder of police officer Don Wilkinson, gunned down while involved in a drugs operation in Mangere last month.

It was revealed at the weekend that Mr Thorne was a convicted killer, having been jailed for the manslaughter of former school friend Rory O'Shea, stabbed to death in Auckland in 1983.

Mr Thorne won sole custody of Caitlin after accusing Richards of snatching her while she was staying with her grandparents during the school holidays on October 7.

Caitlin was handed back to Richards' parents last week, but when Mr Thorne arrived there late last week, Richards hid with Caitlin in a barn and refused to hand her over.

After a tense stand off she was persuaded by police to leave the barn and left the property with Caitlin in a police car.

Police said Caitlin was now with one of her parents.

Mr Thorne's adult daughter Zara Fox flew into Auckland yesterday to support her father at today's custody hearing.

"I think he's a good dad," Ms Fox told TV3 News.

Mr Thorne, now a personal trainer, said he regretted the 1983 incident in Newton, Auckland.

"But I think my actions speak louder than those words, and I've shown myself to be a good dad," he said.

"I just do everything possible to give her a better life."