  Using 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)
$n^\alpha$ with $\alpha \geq 0$ ($\alpha=0$ and $\alpha=1$ 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.
