  We prove that if a unimodular random rooted graph is recurrent, the number of
ends of its uniform spanning tree is almost surely equal to the number of ends
of the graph. Together with previous results in the transient case, this
completely resolves the problem of the number of ends of wired uniform spanning
forest components in unimodular random rooted graphs and confirms a conjecture
of Aldous and Lyons (2006).
