Packing random graphs and hypergraphs
  We determine to within a constant factor the threshold for the property that two random k-uniform hypergraphs with edge probability p have an edge-disjoint packing into the same vertex set. More generally, we allow the hypergraphs to have different densities. In the graph case, we prove a stronger result, on packing a random graph with a fixed graph. 
B\'ela Bollob\'as, Svante Janson, Alex Scott
math.CO