We study probability measure preserving (p.m.p.) non-free actions
of free groups and the associated IRS's. The perfect kernel of a
countable group Gamma is the largest closed subspace of the space
of subgroups of Gamma without isolated points. We introduce the
class of totipotent ergodic p.m.p. actions of Gamma: those for
which almost every point-stabilizer has dense conjugacy class in
the perfect kernel. Equivalently, the support of the associated
IRS is as large as possible, namely it is equal to the whole
perfect kernel. We prove that every ergodic p.m.p. equivalence
relation R of cost