A man hired to find missing 6-year-old Que Langdon believes her father might be trying to sail her to Australia.
Alan Langdon and his daughter have not been heard from since setting off in a catamaran from Kawhia, on the Waikato coast, on 17 December.
Police said today they were looking at a multitude of possible scenarios for the disappearance. They were continuing the search and want help from the public, especially boaties, for sightings of the boat.
The girl's Swiss mother, Ariane Wyler, who is based in Golden Bay, near Nelson, said she was desperate to be reunited with her daughter.
She has hired Child Recovery Services contractor Col Chapman to help the search.
Mr Chapman told RNZ it was possible Mr Langdon, an Australian citizen with family in New Zealand, was trying to make it back to Australia.
He said he no longer believed Mr Langdon's voyage was an innocent sailing trip but, he alleged, another attempt to take Que to elude the family court system.
Mr Chapman said the lack of contact was at the stage of being highly unusual, even for an experienced sailor like Mr Langdon.
He said it was possible they had a mishap at sea or were hiding somewhere in coastal New Zealand. If they were trying to cross the Tasman they would have run out of water by now. He said he planned to arrange a light plane search of the West Coast down to Stewart Island.
He said Mr and Ms Langdon separated close to two years ago after a cyclone that struck Vanuatu destroyed their boat.
Mr Chapman said Ms Wyler's attempts to reach a custody agreement failed. A legal process started, but Mr Langdon allegedly fled to New Zealand with Que, where further court proceedings started.
He said Que was familiar with boats, having been raised on one.
When Mr Langdon and Que set out, they were said to be bound for the Bay of Islands.
Waikato harbourmaster Chris Bredenbeck saw the catamaran leave Kawhia at high tide when the weather was fine, although there had been high winds since.
Air Force plane joins search
A Royal New Zealand Air Force P-3K2 Orion surveillance aircraft has joined the search for the missing six-metre catamaran.
The New Zealand Defence Force said last night it would search the West Coast, from Wellington to North Cape.
The boat was described as white, with blue anti-fouling paint under the waterline, with the sail number T878.
Police said the boat could have gone anywhere from the West Coast of the North Island to North Cape and down the eastern coastline.
Sergeant Warren Shaw said earlier Mr Langdon was an experienced sailor and it was not unusual for him to to head out and not be in contact.
Maritime New Zealand had broadcast all-stations calls asking for sightings.