a) (Left) black hole mass function at z< 0.5 built up by interaction-driven accretion (solid line) and by BH accretion due to disc instabilities (dashed line). The shaded region defines the spread in observational estimates obtained using different methods, as compiled by Shankar et al. (2009). b) (Right) local relation between the BH mass and the total stellar content of galaxies is compared with data. 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 objects as a function of M_BH for any given value of M_∗, as indicated by the bar.