  The distribution of the hypervolume $V$ and surface $\partial V$ of convex
hulls of (multiple) random walks in higher dimensions are determined
numerically, especially containing probabilities far smaller than $P =
10^{-1000}$ to estimate large deviation properties. For arbitrary dimensions
and large walk lengths $T$, we suggest a scaling behavior of the distribution
with the length of the walk $T$ similar to the two-dimensional case, and
behavior of the distributions in the tails. We underpin both with numerical
data in $d=3$ and $d=4$ dimensions. Further, we confirm the analytically known
means of those distributions and calculate their variances for large $T$.
