  A h-uniform hypergraph H=(V,E) is called (l,k)-orientable if there exists an
assignment of each hyperedge e to exactly l of its vertices such that no vertex
is assigned more than k hyperedges. Let H_{n,m,h} be a hypergraph, drawn
uniformly at random from the set of all h-uniform hypergraphs with n vertices
and m edges. In this paper, we determine the threshold of the existence of a
(l,k)-orientation of H_{n,m,h} for k>=1 and h>l>=1, extending recent results
motivated by applications such as cuckoo hashing or load balancing with
guaranteed maximum load. Our proof combines the local weak convergence of
sparse graphs and a careful analysis of a Gibbs measure on spanning subgraphs
with degree constraints. It allows us to deal with a much broader class than
the uniform hypergraphs.
