  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)
