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In this paper we explore a possible route of black hole seed formation thatappeal to a model by Davies, Miller & Bellovary who considered the case of thedynamical collapse of a dense cluster of stellar black holes subjected to aninflow of gas. Here, we explore this case in a broad cosmological context. Theworking hypotheses are that (i) nuclear star clusters form at high redshifts inpre-galactic discs hosted in dark matter halos, providing a suitableenvironment for the formation of stellar black holes in their cores, (ii) majorcentral inflows of gas occur onto these clusters due to instabilities seeded inthe growing discs and/or to mergers with other gas-rich halos, and that (iii)following the inflow, stellar black holes in the core avoid ejection due to thesteepening to the potential well, leading to core collapse and the formation ofa massive seed of $<~ 1000\, \rm M_\odot$. We simulate a cosmological boxtracing the build up of the dark matter halos and there embedded baryons, andexplore cluster evolution with a semi-analytical model. We show that this routeis feasible, peaks at redshifts $z <~ 10$ and occurs in concomitance with theformation of seeds from other channels. The channel is competitive relative toothers, and is independent of the metal content of the parent cluster. Thismechanism of gas driven core collapse requires inflows with masses at least tentimes larger than the mass of the parent star cluster, occurring on timescalesshorter than the evaporation/ejection time of the stellar black holes from thecore. In this respect, the results provide upper limit to the frequency of thisprocess.

Constraining the high redshift formation of black hole seeds in nuclear star clusters with gas inflows