  We summarize a study where we test the hypothesis that local black holes (BH)
are relics of AGN activity. We compare the mass function of BHs in the local
universe with that expected from AGN relics, which are BHs grown entirely with
mass accretion during AGN phases. The local BH mass function (BHMF) is
estimated by applying the well-known correlations between BH mass, bulge
luminosity and stellar velocity dispersion to galaxy luminosity and velocity
functions. The density of BHs in the local universe is 4.6 (-1.4;+1.9) 10^5
Msun Mpc-3. The relic BHMF is derived from the continuity equation with the
only assumption that AGN activity is due to accretion onto massive BHs and that
merging is not important. We find that the relic BHMF at z=0 is generated
mainly at z<3. Moreover, the BH growth is anti-hierarchical in the sense that
smaller BHs (MBH<10^7 Msun) grow at lower redshifts (z<1) with respect to more
massive ones (z~1-3). Unlike previous work, we find that the BHMF of AGN relics
is perfectly consistent with the local BHMF indicating the local BHs were
mainly grown during AGN activity. This agreement is obtained while satisfying,
at the same time, the constraints imposed by the X-ray background. The
comparison with the local BHMF also suggests that the merging process is not
important in shaping the relic BHMF, at least at low redshifts (z<3). Our
analysis thus suggests the following scenario: local BHs grew during AGN phases
in which accreting matter was converted into radiation with efficiencies
eff=0.04-0.16 and emitted at a fraction lambda=0.1-1.7 of the Eddington
luminosity. The average total lifetime of these active phases ranges from ~4.5
10^8 yr for MBH<10^7 Msun to ~1.5 10^8 yr for MBH>10^9 Msun.
