We show that for a transitive unimodular graph, the number of ends is the same for every tree of the free minimal spanning forest. This answers a question of Lyons, Peres and Schramm.
"Ends in free minimal spanning forests." Ann. Probab. 34 (3) 865 - 869, May 2006. https://doi.org/10.1214/009117906000000025