A set of graphs is said to pack into the complete graph, K_n, if
the graphs can be found as edge-disjoint subgraphs of K_n. The Gy'arf'as
tree packing conjecture states that any set of $n-1$ trees $T_{n}, T_{n-1},
dots, T_{2}$ such that $T_i$ has $i$ vertices pack into $K_n$. Even when
we weaken the statement to claim that the largest t>3 trees T_{n}, T_{n-1},
dots , T_{n-t+1} the conjecture remains open. Among others we will discuss
our recent result that any t=(1/10)n^{1/4} trees T_{n}, T_{n-1}, dots ,
T_{n-t+1} pack into K_{n+1} (for n large
enough). (Joint work with J. Balogh.)