Local M_BH − M_∗ relation for the IT model (left panels) and the DI model (right panels). Data points represent the observed local relation from Häring & Rix (2004, diamonds), and Marconi & Hunt (2003, squares, here M_∗ is derived using the best-fitting virial relation of Cappellari et al. 2006); the colour code represents the fraction of AGN as a function of M_BH for any given value of M_∗, as indicated by the colour bar. We also show some of the paths in the M_BH(t) − M_∗(t) plane followed, during their evolution, by BHs (and by their host galaxies) reaching a final mass of M_BH(z = 0) ≥ 10⁹ M_⊙.