2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231026We provide information about the asymptotic regimes for a homogeneous fragmentation of a finite set. We establish a phase transition for the asymptotic behaviours of the shattering times, defined as the first instants when all the blocks of the partition process have cardinality less than a fixed integer. Our results may be applied to the study of certain random split trees.Probability60F15, 60J80.text