I present a new method to unveil the history of cosmic accretion and the build-up of supermassive black holes in the nuclei of galaxies , based on observations of the evolving radio and ( hard ) X-ray luminosity functions of active galactic nuclei .
The fundamental plane of black hole activity discovered by Merloni , Heinz & Di Matteo ( 2003 ) , which defines a universal correlation among black hole mass ( M ) , 2-10 keV X-ray luminosity and 5 GHz radio luminosity is used as a mass and accretion rate estimator , provided a specific functional form for the dependency of the X-ray luminosity on the dimensionless accretion rate \dot { m } is assumed .
I adopt the local black hole mass function as derived from the velocity dispersion ( \sigma ) distributions of nearby galaxies coupled with the M - \sigma relation as a boundary condition to integrate backwards in time the continuity equation for the supermassive black holes evolution , neglecting the role of mergers in shaping up the black hole mass function .
Under the most general assumption that , independently on M , black hole accretion proceeds in a radiatively efficient way above a certain rate , and in a radiatively inefficient way below , the redshift evolution of the black hole mass function and the black hole accretion rate function ( i.e .
the distribution of the Eddington scaled accretion rates for objects of any given mass ) are calculated self-consistently .
The only tunable parameters are the overall efficiency of extracting gravitational energy from the accreting gas , \epsilon , and the critical ratio of the X-ray to Eddington luminosity , L _ { 2 - 10 keV,cr } / L _ { Edd } \equiv x _ { cr } , at which the transition between accretion modes takes place .
For fiducial values of these parameters ( \epsilon = 0.1 and x _ { cr } = 10 ^ { -3 } ) , I found that half ( \sim 85 % ) of the local black hole mass density was accumulated at redshift z < 1 ( z < 3 ) , mostly in radiatively efficient episodes of accretion .
The evolution of the black hole mass function between z = 0 and z \sim 3 shows clear signs of an anti-hierarchical behaviour : while the majority of the most massive objects ( M \ga 10 ^ { 9 } ) were already in place at z \sim 3 , lower mass ones mainly grew at progressively lower redshift , so that the average black hole mass increases with increasing redshift .
Also , the average accretion rate decreases towards lower redshift .
Consequently , sources in the radiatively inefficient regime of accretion only begin to dominate the comoving accretion energy density in the universe at z < 1 ( with the exact value of z 
depending on x _ { cr } ) , while at the peak of the black hole accretion rate history , radiatively efficient accretion dominates by almost an order of magnitude .
I will discuss the implications of these results for the efficiency of accretion onto SMBH , the quasars lifetimes and duty cycles , the history of AGN feedback in the form of mechanical energy output and , more generally , for the cosmological models of structure formation in the universe .