  Let \Fc be a holomorphic foliation by curves defined in a neighborhood of 0
in \C^2 having 0 as a hyperbolic singularity. Let T be a harmonic current
directed by \Fc which does not give mass to any of the two separatrices. Then
we show that the Lelong number of T at 0 vanishes. Next, we apply this local
result to investigate the global mass-distribution for directed harmonic
currents on singular holomorphic foliations living on compact complex surfaces.
Finally, we apply this global result to study the recurrence phenomenon of a
generic leaf.
