  Consider a random directed graph on $n$ vertices with independent identically
distributed outdegrees with distribution $F$ having mean $\mu$, and
destinations of arcs selected uniformly at random. We show that if $\mu >1$
then for large $n$ there is very likely to be a unique giant strong component
with proportionate size given as the product of two branching process survival
probabilities, one with offspring distribution $F$ and the other with Poisson
offspring distribution with mean $\mu$. If $\mu \leq 1$ there is very likely to
be no giant strong component. We also extend this to allow for $F$ varying with
$n$.
