Two channels of supermassive black hole growth as seen on the galaxies mass-size plane

[Abridged] 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. This is expected from the negligible scatter previously reported in the virial mass estimator sigma^2=GxMstar/(5xRe). We show that, when describing the black hole mass distribution non-parametrically using the Locally Weighted Regression method, all the black hole mass variation happens along lines of constant velocity dispersion on the (Mstar, Re) plane, or Mstar $\propto$ Re for Mstar 2x10^11 Msun. This behaviour can be explained assuming that Mbh in galaxies less massive than a critical mass can be predicted by the Mbh - sigma relation, while black holes in more massive galaxies follow a modified relation which is also dependent on Mstar once Mstar is larger than the critical mass. We argue that the critical mass is Mcrit ~ 2x10^11 Msun, the same critical mass that divides galaxies in mass - size plane based on their other properties and, particularly, separates fast and regularly rotating galaxies from slow rotators with deficits in central surface brightness profiles. This behaviour of Mbh is consistent with the current scenario of galaxy evolution where the majority of galaxies grow through star formation, while the most massive galaxies, typically in more dense environments, undergo a sequence of dissipation-less mergers.