  The Gy\'arf\'as tree packing conjecture asserts that any set of trees with
$2,3, ..., k$ vertices has an (edge-disjoint) packing into the complete graph
on $k$ vertices. Gy\'arf\'as and Lehel proved that the conjecture holds in some
special cases. We address the problem of packing trees into $k$-chromatic
graphs. In particular, we prove that if all but three of the trees are stars
then they have a packing into any $k$-chromatic graph. We also consider several
other generalizations of the conjecture.
