  Supermassive black holes (BHs) of millions solar masses and above reside in
the center of most local galaxies, but they also power active galactic nuclei
and quasars, detected up to z=7. This observational evidence puts strong
constraints on the BH growth and the mass of the first BH seeds. The scenario
of "direct collapse" is very appealing as it leads to the formation of large
mass BH seeds in the range 10^4-10^6 Msun, which eases explaining how quasars
at z=6-7 are powered by BHs with masses >10^9 Msun. Direct collapse, however,
appears to be rare, as the conditions required by the scenario are that gas is
metal-free, the presence of a strong photo-dissociating Lyman-Werner flux, and
large inflows of gas at the center of the halo, sustained for 10-100 Myr. We
performed several cosmological hydrodynamical simulations that cover a large
range of box sizes and resolutions, thus allowing us to understand the impact
of several physical processes on the distribution of direct collapse BHs. We
identify halos where direct collapse can happen, and derive the number density
of BHs. We also investigate the discrepancies between hydrodynamical
simulations, direct or post-processed, and semi-analytical studies. We find
that for direct collapse to account for BHs in normal galaxies, the critical
Lyman-Werner flux required for direct collapse must be much less than predicted
by 3D simulations that include detailed chemical models. However, when
supernova feedback is relatively weak, enough direct collapse BHs to explain
z=6-7 quasars can be obtained for more realistic values of the critical Lyman
Werner flux.
