  We prove that every component of the wired uniform spanning forest (WUSF) is
one-ended almost surely in every transient reversible random graph, removing
the bounded degree hypothesis required by earlier results. We deduce that every
component of the WUSF is one-ended almost surely in every supercritical
Galton-Watson tree, answering a question of Benjamini, Lyons, Peres and
Schramm.
  Our proof introduces and exploits a family of Markov chains under which the
oriented WUSF is stationary, which we call the wired cycle-breaking dynamics.
