The presence of massive black holes (BHs) with masses of order $10^9rm, M_odot$, powering bright quasars when the Universe was less than 1 Gyr old, poses strong constraints on their formation mechanism. Several scenarios have been proposed to date to explain massive BH formation, from the low-mass seed BH remnants of the first generation of stars to the massive seed BHs resulting from the rapid collapse of massive gas clouds. However, the plausibility of some of these scenarios to occur within the progenitors of high-z quasars has not yet been thoroughly explored. In this work, we investigate, by combining dark-matter only N-body simulations with a semi-analytic framework, whether the conditions for the formation of massive seed BHs from synchronised atomic-cooling halo pairs and/or dynamically-heated mini-haloes are fulfilled in the overdense regions where the progenitors of a typical high-redshift quasar host form and evolve. Our analysis shows that the peculiar conditions in such regions, i.e. strong halo clustering and high star formation rates, are crucial to produce a non-negligible number of massive seed BH host candidates: we find $approx1400$ dynamically heated metal-free mini-haloes, including one of these which evolves to a synchronised pair and ends up in the massive quasar-host halo by $z=6$. This demonstrates that the progenitors of high-redshift quasar host haloes can harbour early massive seed BHs. Our results further suggest that multiple massive seed BHs may form in or near the quasar hosts progenitors, potentially merging at lower redshifts and yielding gravitational wave events.
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