  The Bar\'at-Thomassen conjecture asserts that for every tree $T$ on $m$
edges, there exists a constant $k_T$ such that every $k_T$-edge-connected graph
with size divisible by $m$ can be edge-decomposed into copies of $T$. So far
this conjecture has only been verified when $T$ is a path or when $T$ has
diameter at most 4. Here we prove the full statement of the conjecture.
