  Let $\Sigma$ be a closed surface other than the sphere, the torus, the
projective plane or the Klein bottle. We construct a continuum of p.m.p.
ergodic minimal profinite actions for the fundamental group of $\Sigma$, that
are topologically free but not essentially free, a property that we call
allostery. Moreover, the IRS's we obtain are pairwise distincts.
