Let G and H be k-graphs (k-uniform hypergraphs); then a perfect
H-packing in G is a collection of vertex-disjoint copies of H in G
which together cover every vertex of G. For any fixed H let δ(H,n)
be the minimum δ such that any k-graph G on n vertices with
minimum codegree δ(G)≥δ contains a perfect H-packing. The
problem of determining δ(H,n) has been widely studied for graphs (i.e.
2-graphs), but little is known for k≥3. Here we determine the
asymptotic value of δ(H,n) for all complete k-partite k-graphs H,
as well as a wide class of other k-partite k-graphs. In particular, these
results provide an asymptotic solution to a question of R\"odl and Ruci\'nski
on the value of δ(H,n) when H is a loose cycle. We also determine
asymptotically the codegree threshold needed to guarantee an H-packing
covering all but a constant number of vertices of G for any complete
k-partite k-graph H.Comment: v2: Updated with minor corrections. Accepted for publication in
Journal of Combinatorial Theory, Series