We investigate the role of supermassive black holes in the global context of galaxy evolution by measuring the host galaxy stellar mass function (HGMF) and the specific accretion rate i.e., lambda_SAR, distribution function (SARDF) up to z~2.5 with ~1000 X-ray selected AGN from XMM-COSMOS. Using a maximum likelihood approach, we jointly fit the stellar mass function and specific accretion rate distribution function, with the X-ray luminosity function as an additional constraint. Our best fit model characterizes the SARDF as a double power-law with mass dependent but redshift independent break whose low lambda_SAR slope flattens with increasing redshift while the normalization increases. This implies that, for a given stellar mass, higher lambda_SAR objects have a peak in their space density at earlier epoch compared to the lower lambda_SAR ones, following and mimicking the well known AGN cosmic downsizing as observed in the AGN luminosity function. The mass function of active galaxies is described by a Schechter function with a almost constant Mstar* and a low mass slope alpha that flattens with redshift. Compared to the stellar mass function, we find that the HGMF has a similar shape and that, up to log((Mstar/Msun)~11.5 the ratio of AGN host galaxies to star forming galaxies is basically constant (~10%). Finally, the comparison of the AGN HGMF for different luminosity and specific accretion rate sub-classes with the phenomenological model prediction by Peng et al. (2010) for the "transient" population, i.e. galaxies in the process of being mass-quenched, reveals that low-luminosity AGN do not appear to be able to contribute significantly to the quenching and that at least at high masses, i.e. Mstar>10^(10.7) Msun , feedback from luminous AGN (log(Lbol)>~46 [erg/s]) may be responsible for the quenching of star formation in the host galaxy.

15 pages, 10 figures, accepted for publication in A&A