Perfectly packing graphswith bounded degeneracy and many leaves

We prove that one can perfectly pack degenerate graphs into complete or dense n-vertex quasirandom graphs, provided that all the degenerate graphs have maximum degree o(n/log n), and in addition omega(n) of them have at most (1-omega(1))n vertices and omega(n) leaves. This proves Ringel's conjecture and the Gy & aring;rf & aring;s Tree Packing Conjecture for all but an exponentially small fraction of trees (or sequences of trees, respectively).