We present a comprehensive synthesis model for the AGN evolution and the growth of supermassive black holes in the Universe. We solve the continuity equation for SMBH mass function using the locally determined one as a boundary condition, and the hard X-ray luminosity function as tracer of the AGN growth rate distribution, supplemented with a luminosity-dependent bolometric correction and an absorbing column distribution. Differently from most previous semi-analytic and numerical models, we do not assume any specific distribution of Eddington ratios, rather we determine it empirically by coupling the mass and luminosity functions. SMBH show a very broad accretion rate distribution, and we discuss the consequences of this fact for our understanding of observed AGN fractions in galaxies. We confirm previous results and demonstrate that, at least for z<1.5, SMBH mass function evolves anti-hierarchically, i.e. the most massive holes grew earlier and faster than less massive ones. For the first time, we find hints of a reversal of such a downsizing behaviour at redshifts above the peak of the black hole accretion rate density (z~2). We also derive tight constraints on the (mass weighted) average radiative efficiency of AGN: we find that 0.065<xi_0 epsilon_{rad}< 0.07$, where xi_0 is the local SMBH mass density in units of 4.3x10^5 M_sun Mpc^{-3}. We trace the cosmological evolution of the kinetic luminosity function of AGN, and find that the overall efficiency of SMBH in converting accreted rest mass energy into kinetic power, ranges between 3 and 5 times 10^{-3}. Such a ``kinetic efficiency varies however strongly with SMBH mass and redshift, being maximal for very massive holes at late times, as required for the AGN feedback by many galaxy formation models in Cosmological contexts. (Abriged)
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