  Recent transport measurements on thin graphite films grown on SiC show large
coherence lengths and anomalous integer quantum Hall effects expected for
isolated graphene sheets. This is the case eventhough the layer-substrate
epitaxy of these films implies a strong interface bond that should induce
perturbations in the graphene electronic structure. Our DFT calculations
confirm this strong substrate-graphite bond in the first adsorbed carbon layer
that prevents any graphitic electronic properties for this layer. However, the
graphitic nature of the film is recovered by the second and third absorbed
layers. This effect is seen in both the (0001)and $(000\bar{1})$ 4H SiC
surfaces. We also present evidence of a charge transfer that depends on the
interface geometry. It causes the graphene to be doped and gives rise to a gap
opening at the Dirac point after 3 carbon layers are deposited in agreement
with recent ARPES experiments (T.Ohta et al, Science {\bf 313} (2006) 951).
