It has hitherto been known that in a transitive unimodular graph, each tree in the wired spanning forest has only one end a.s. We dispense with the assumptions of transitivity and unimodularity, replacing them with a much broader condition on the isoperimetric profile that requires just slightly more than uniform transience.
"Ends in Uniform Spanning Forests." Electron. J. Probab. 13 1702 - 1725, 2008. https://doi.org/10.1214/EJP.v13-566