A polyamorous ex-throuple fighting over how to split a valuable Auckland property have taken their battle to the Supreme Court.

The court will determine whether the Family Court has any jurisdiction to determine relationship property claims for polyamorous relationships.

In the first case of its kind in New Zealand, the High Court earlier ruled the Property Relationships Act (PRA) could not be applied to people in a multi-partner relationship.

But the Court of Appeal overturned that ruling in 2021 and the matter has now been further appealed.

The case relates to a couple, Lilach and Brett Paul, who married in 1993.

In 1999, Lilach met Fiona Mead and in 2002 the three of them formed a polyamorous relationship.

They moved into a 4ha property in Kumeu, which had just been purchased in Mead's name for $533,000. She paid the deposit of $40,000.

They lived together at the property for 15 years, and mostly shared the same room and bed, court documents said.

All three worked and contributed to the household until 2017 when Lilach broke up with Mead and Brett, who in turn broke up in 2018, with Mead continuing to live at the property.

The property had by then risen in value to more than $2 million.

Lilach applied to the Family Court to determine her share in the property, but the Family Court referred the case to the High Court.

The Supreme Court appeal is being heard in Wellington this morning.

In written submissions, Mead's lawyer said the Court of Appeal correctly recognised the PRA was premised on the notion of "coupledom".

"This is reflected in Parliament's explicit and pervasive use of dyadic terminology."

But in the Court of Appeal's decision to recharacterise their relationship as three couple relationships, it "undermined and misconstrued the essential nature of their relationship, that being a threesome".

Mead's lawyer also said the court's reliance on certain provisions in the PRA was misplaced, as the provisions had been regularly criticised as "not fit for purpose".

"They are not intended to apply to, and cannot be legitimately deployed as means to bring within the PRA, polyamorous relationships."

Extending the PRA to cover polyamorous relationships was a matter best left for Parliament, the lawyer argued.

Written submissions for Lilach said she was trespassed from the "family home" after she broke up with Mead.

Lilach's lawyer said the PRA's definition of a de facto relationship was "broad, flexible, and evaluative".

"It is not concerned with how the parties describe themselves but with whether the relationship has the requisite characteristics. In this case, the polyamorous relationship between the parties was comprised of three qualifying relationships."

They also said the Bill of Rights Act supported a reading of the PRA "consistent with the right to freedom from discrimination on the ground of family status".

There should be no practical impediment to dividing the property equally, so long as there were qualifying relationships.

"Excluding multi-partnered relationships from the definition of a de facto relationship would have serious implications, such as inadvertently ending a marriage once there is involvement of a third party."

The hearing is set down for one day.