  Considering the wired uniform spanning forest on a nonunimodular transitive
graph, we show that almost surely each tree of the wired uniform spanning
forest is light. More generally we study the tilted volumes for the trees in
the wired uniform spanning forest.
  Regarding the free uniform spanning forest, we consider several families of
nonunimodular transitive graphs. We show that the free uniform spanning forest
is the same as the wired one on Diestel--Leader graphs. For grandparent graphs,
we show that the free uniform spanning forest is connected and has branching
number bigger than one. We also show that each tree of the free uniform
spanning forest is heavy and has branching number bigger than one on a free
product of a nonunimodular transitive graph with one edge when the free uniform
spanning forest is not the same as the wired.
