  We investigate the variation of black hole masses (Mbh) as a function of
their host galaxy stellar mass (Mstar) and half-light radius (Re). We confirm
that the scatter in Mbh within this plane is essentially the same as that in
the Mbh - sigma relation, as expected from the negligible scatter reported in
the virial mass estimator sigma_v^2=GxMstar/(5xRe). All variation in Mbh
happens along lines of constant sigma_v on the (Mstar, Re) plane, or Mstar
$\propto$ Re for Mstar <2x10^11 Msun. This trend is qualitatively the same as
those previously reported for galaxy properties related to stellar populations,
like age, metallicity, alpha enhancement, mass-to-light ratio and gas content.
We find evidence for a change in the Mbh variation above the critical mass of
Mcrit ~ 2x10^11 Msun. This behaviour can be explained assuming that Mbh in
galaxies less massive than Mcrit can be predicted by the Mbh - sigma relation,
while Mbh in more massive galaxies follow a modified relation which is also
dependent on Mstar once Mstar >Mcrit. This is consistent with the scenario
where the majority of galaxies grow through star formation, while the most
massive galaxies undergo a sequence of dissipation-less mergers. In both
channels black holes and galaxies grow synchronously, giving rise to the black
hole - host galaxy scaling relations, but there is no underlying single
relation that is universal across the full range of galaxy masses.
