2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124729A class of random discrete distributions $P$ is introduced by means of a recursive splitting of unity. Assuming supercritical branching, we show that for partitions induced by sampling from such $P$ a power growth of the number of blocks is typical. Some known and some new partition structures appear when $P$ is induced by a Dirichlet splitting.Published at http://dx.doi.org/10.1214/009117906000000584 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability60G09, 60C05 (Primary)text