  We obtain several results about stability of the Bergman kernel on a tower of
coverings on complex manifolds. An effective version of Rhodes' result is given
for a tower of coverings on a compact Riemann surface of genus greater than or
equal to 2. Stability of the Bergman kernel is established for towers of
coverings on hyperbolic Riemann surfaces and on complete Kaehler manifolds
satisfying certain potential conditions. As a consequence, stability of the
Bergman kernel is established for any tower of coverings of Riemann surfaces
when the top manifold is simply-connected.
