  The second layer of He-4 adsorbed on a graphite substrate is studied by
Quantum Monte Carlo simulations. We make use of a microscopic model of the
substrate fully accounting for its corrugation, and compare the results to
those obtained with a smooth substrate. The only effect of corrugation is a
~20% reduction of the value of the superfluid fraction of the top layer, in the
limit of zero temperature. No evidence of any commensurate (7/12) crystalline
and/or "supersolid" phase is found; the superfluid transition temperature is
estimated to be ~ 0.75 K. We discuss the implication of these findings on the
interpretation of recent experiments.
