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Supermassive black holes (BHs) of millions solar masses and above reside inthe center of most local galaxies, but they also power active galactic nucleiand quasars, detected up to z=7. This observational evidence puts strongconstraints on the BH growth and the mass of the first BH seeds. The scenarioof "direct collapse" is very appealing as it leads to the formation of largemass BH seeds in the range 10^4-10^6 Msun, which eases explaining how quasarsat 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 ismetal-free, the presence of a strong photo-dissociating Lyman-Werner flux, andlarge inflows of gas at the center of the halo, sustained for 10-100 Myr. Weperformed several cosmological hydrodynamical simulations that cover a largerange of box sizes and resolutions, thus allowing us to understand the impactof several physical processes on the distribution of direct collapse BHs. Weidentify halos where direct collapse can happen, and derive the number densityof BHs. We also investigate the discrepancies between hydrodynamicalsimulations, direct or post-processed, and semi-analytical studies. We findthat for direct collapse to account for BHs in normal galaxies, the criticalLyman-Werner flux required for direct collapse must be much less than predictedby 3D simulations that include detailed chemical models. However, whensupernova feedback is relatively weak, enough direct collapse BHs to explainz=6-7 quasars can be obtained for more realistic values of the critical LymanWerner flux.

On the number density of "direct collapse" black hole seeds