  We show that, if $H$ is a random subgroup of a finitely generated free group
$F_k$, only inner automorphisms of $F_k$ may leave $H$ invariant. A similar
result holds for random subgroups of toral relatively hyperbolic groups, more
generally of groups which are hyperbolic relative to slender subgroups. These
results follow from non-existence of splittings over slender groups which are
relative to a random group element. Random subgroups are defined using random
walks or balls in a Cayley tree of $F_k$.
