  For a general class of elliptic PDE's in mean field form on compact Riemann
surfaces with exponential nonlinearity, we address the question of the
existence of solutions with concentrated nonlinear term, which, in view of the
applications, are physically of definite interest. In the model, we also
include the possible presence of singular sources in the form of Dirac masses,
which makes the problem more degenerate and difficult to attack.
