2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227508For a subfamily of multiplicative measures on integer partitions we give conditions for properly rescaled associated Young diagrams to converge in probability to a certain deterministic curve named the limit shape of partitions. We provide explicit formulas for the scaling function and the limit shape covering some known and some new examples.22 pages; added some references and corrected some typosCombinatoricsProbability05A17; 60B10text