  Let \Fc be a holomorphic foliation by Riemann surfaces on a compact K\"ahler
surface X. Assume it is generic in the sense that all the singularities are
hyperbolic and that the foliation admits no directed positive closed
(1,1)-current. Then there exists a unique (up to a multiplicative constant)
positive \ddc-closed (1,1)-current directed by \Fc. This is a very strong
ergodic property of \Fc. Our proof uses an extension of the theory of densities
to a class of non-\ddc-closed currents. A complete description of the cone of
directed positive \ddc-closed (1,1)-currents is also given when \Fc admits
directed positive closed currents.
