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They applied to the High Court to get a declaration saying this - effectively requiring the council to offer to sell the land back to them at 1980s prices - but were unsuccessful.
They challenged the matter to the Court of Appeal but, again, were unsuccessful.
The appellate court last month ruled the board had a duty to offer the land back to four of the seven descendants, because it had acquired the land for a public work and by 1982 still held but no longer required the land for this purpose.
But Justices Rhys Harrison, Christine French and Jillian Mallon decided not to declare that the council had to offer the land back to the group.
"The descendants had waited too long before bringing their claim, with the consequence that the council has developed the Te Atatu land into residential housing and a public park that was made possible by levying special rates from the community," a summary of the Court of Appeal's decision said.
"The descendants were also not particularly attached to the land. Under agreements they had made with a company that would fund and run this case, the descendants would not keep the land. It would go to the litigation funding company, giving it a windfall because of the substantial difference between the value of the land in the 1980s and its value today," that summary said.
The descendants have now applied for leave to appeal to the Supreme Court, a lawyer involved in the case confirmed.
Litigants do not have an automatic right to take a case to the country's highest court and must seek leave from it to do so.
See the Court of Appeal's decision here: