  We analyse the demographics of black holes (BHs) in the large-volume
cosmological hydrodynamical simulation Horizon-AGN. This simulation
statistically models how much gas is accreted onto BHs, traces the energy
deposited into their environment and, consequently, the back-reaction of the
ambient medium on BH growth. The synthetic BHs reproduce a variety of
observational constraints such as the redshift evolution of the BH mass density
and the mass function. Strong self-regulation via AGN feedback, weak supernova
feedback, and unresolved internal processes result in a tight BH-galaxy mass
correlation. Starting at z~2, tidal stripping creates a small population of BHs
over-massive with respect to the halo. The fraction of galaxies hosting a
central BH or an AGN increases with stellar mass. The AGN fraction agrees
better with multi-wavelength studies, than single-wavelength ones, unless
obscuration is taken into account. The most massive halos present BH
multiplicity, with additional BHs gained by ongoing or past mergers. In some
cases, both a central and an off-centre AGN shine concurrently, producing a
dual AGN. This dual AGN population dwindles with decreasing redshift, as found
in observations. Specific accretion rate and Eddington ratio distributions are
in good agreement with observational estimates. The BH population is dominated
in turn by fast, slow, and very slow accretors, with transitions occurring at
z=3 and z=2 respectively.
