Böttcher–Hladký–Piguet–Taraz tree-packing conjecture

A family of graphs packs into $G$ if $G$ contains pairwise edge-disjoint copies of its members.

Böttcher–Hladký–Piguet–Taraz conjecture. Each family of trees of individual orders at most $n+1$ and total number of edges at most $\binom{2n+1}{2}$ packs into $K_{2n+1}$.

This generalizes Ringel's conjecture. The source says it has been confirmed for large trees with maximum degree $\mathrm{O}(n/\log n)$, but the full statement remains open.