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We prove that one can perfectly pack degenerate graphs into complete or dense$n$-vertex quasirandom graphs, provided that all the degenerate graphs havemaximum degree $o(\frac{n}{\log n})$, and in addition $\Omega(n)$ of them haveat most $(1-\Omega(1))n$ vertices and $\Omega(n)$ leaves. This proves Ringel'sconjecture and the Gy\'arf\'as Tree Packing Conjecture for all but anexponentially small fraction of trees (or sequences of trees, respectively).

Perfectly packing graphs with bounded degeneracy and many leaves