  A $k$-uniform hypergraph $H = (V, E)$ is called $\ell$-orientable, if there
is an assignment of each edge $e\in E$ to one of its vertices $v\in e$ such
that no vertex is assigned more than $\ell$ edges. Let $H_{n,m,k}$ be a
hypergraph, drawn uniformly at random from the set of all $k$-uniform
hypergraphs with $n$ vertices and $m$ edges. In this paper we establish the
threshold for the $\ell$-orientability of $H_{n,m,k}$ for all $k\ge 3$ and
$\ell \ge 2$, i.e., we determine a critical quantity $c_{k, \ell}^*$ such that
with probability $1-o(1)$ the graph $H_{n,cn,k}$ has an $\ell$-orientation if
$c < c_{k, \ell}^*$, but fails doing so if $c > c_{k, \ell}^*$.
  Our result has various applications including sharp load thresholds for
cuckoo hashing, load balancing with guaranteed maximum load, and massive
parallel access to hard disk arrays.
