New Zealand model Sophia Nash could be arrested on arrival if she returns.

An arrest warrant was issued after Ms Nash failed to appear in Auckland District Court on Wednesday on charges of theft, driving while disqualified and breaching a community-work order.

On Friday it was revealed she had left the country with her two children.

Police have tonight confirmed they have placed a border alert on her passport.

"This will alert staff to her status in the event of her return to New Zealand," a police spokesman told the Herald.

It would be up to staff whether or not to arrest Nash upon arrival, he said.

"The potential is there but the staff on the day would have a certain amount of discretion."

Police declined to comment further on whether they had made contact with Nash, saying the investigation was ongoing.

Nash was due to appear in court over allegations she stole a $20 Christian Dior handbag from a Mt Eden Salvation Army story, something she denies.

Police allege she was then caught driving on Dominion Rd while disqualified. An arrest warrant was issued for her after she didn't show up at court.

Nash has also denied she left the country because of the court case, saying she had planned to leave and start a new life for her and her daughters Honey and Lola.

The girls' father, Nash's estranged husband, George FM DJ Thane Kirby, played his regular DJ spot at Ponsonby Rd's Chapel Bar and Bistro this afternoon, despite his personal troubles.

In a social media post on Friday, since removed, Mr Kirby said things were difficult at the moment.

"Put quite simply this is a really hard time for me and my family right now. My ex-wife has left the country and has taken our children with her.

"I'm devastated but kinda powerless to do anything other than put this matter in the hands of my lawyer, police and Cyfs. I want to thank those close to me for their support it really means a lot.

"I'm just wishing for my girls to come home as quickly as possible so we can put this terrible period behind us once and for all."