  We show that if a group $G$ acting faithfully on a rooted tree $T$ has a free
subgroup, then either there exists a point $w$ of the boundary $\partial T$ and
a free subgroup of $G$ with trivial stabilizer of $w$, or there exists
$w\in\partial T$ and a free subgroup of $G$ fixing $w$ and acting faithfully on
arbitrarily small neighborhoods of $w$. This can be used to prove absence of
free subgroups for different known classes of groups. For instance, we prove
that iterated monodromy groups of expanding coverings have no free subgroups
and give another proof of a theorem by S. Sidki.
