2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74261Using recent results on singularity analysis for Hadamard products of generating functions, we obtain the limiting distributions for additive functionals on $m$-ary search trees on $n$ keys with toll sequence (i) $n^α$ with $α\geq 0$ ($α=0$ and $α=1$ correspond roughly to the space requirement and total path length, respectively); (ii) $\ln \binom{n}{m-1}$, which corresponds to the so-called shape functional; and (iii) $\mathbf{1}_{n=m-1}$, which corresponds to the number of leaves.26 pages; v2 expands on the introduction by comparing the results with other probability modelsProbabilityCombinatorics68W40 (Primary) 60F05, 60C05 (Secondary)text