Land Tenure in the Cook Islands
If a right-holder died without male issue, his rights normally fell to those who held in common with him. For page 93 example, if the man had surviving brothers who shared the land with him, then his rights fell to them and their issue. Alternatively, the rights could pass through a daughter to his grandson, and instances of this occurring were common. In the event of there being neither siblings nor issue, the rights were traced back to the source whence they came, and from there to the nearest surviving relative. If no such relatives were traceable, then the land reverted to the chief of the lineage until such time as he chose to allot it to some needful member. As there was no rigid set of priorities for inheritance in cases where there were neither issue nor resident siblings, the way was left open for a number of lesser claimants, and the settlement of their various claims, being so nebulously based, was conducive to dispute.
It is not likely that many whole lineages died out, for if numbers were dwindling too low, new members could be adopted, or the waning lineage could merge with a contiguous (and undoubtedly related) lineage.1 A lineage with few members presumably had relatively extensive land resources and was thus well situated to arrange uxorilocal marriages and increase its strength by this means.
1 This may have been done either voluntarily or under pressure. Strong neighbours would be tempted to spread into vacant lands, and a voluntary merger may have been preferable to the possibility of loss by force.