  We consider a well known model of random directed acyclic graphs of order
$n$, obtained by recursively adding vertices, where each new vertex has a fixed
outdegree $d\ge2$ and the endpoints of the $d$ edges from it are chosen
uniformly at random among previously existing vertices.
  Our main results concern the number $X$ of vertices that are descendants of
$n$. We show that $X/\sqrt n$ converges in distribution; the limit distribution
is, up to a constant factor, given by the $d$th root of a Gamma distributed
variable. $\Gamma(d/(d-1))$. When $d=2$, the limit distribution can also be
described as a chi distribution $\chi(4)$. We also show convergence of moments,
and find thus the asymptotics of the mean and higher moments.
