  We present results of simulations aimed at tracing the formation of nuclear
star clusters (NCs) and black hole (BH) seeds, in a cosmological context. We
focus on two mechanisms for the formation of BHs at high redshifts: as
end-products of (1) Population III stars in metal free halos, and of (2)
runaway stellar collisions in metal poor NCs. Our model tracks the chemical,
radiative and mechanical feedback of stars on the baryonic component of the
evolving halos. This procedure allows us to evaluate when and where the
conditions for BH formation are met, and to trace the emergence of BH seeds
arising from the dynamical channel, in a cosmological context. BHs start to
appear already at z~30 as remnants of Population III stars. The efficiency of
this mechanism begins decreasing once feedbacks become increasingly important.
Around redshift z~15, BHs mostly form in the centre of mildly metal enriched
halos inside dense NCs. The seed BHs that form along the two pathways have at
birth a mass around 100-1000M\odot. The occupation fraction of BHs is a
function of both halo mass and mass growth rate: at a given z, heavier and
faster growing halos have a higher chance to form a native BH, or to acquire an
inherited BH via merging of another system. With decreasing z, the probability
of finding a BH shifts toward progressively higher mass halo intervals. This is
due to the fact that, at later cosmic times, low mass systems rarely form a
seed, and already formed BHs are deposited into larger mass systems due to
hierarchical mergers. Our model predict that at z=0, all halos above
10^11M\odot should host a BH (in agreement with observational results), most
probably inherited during their lifetime. Halos less massive then 10^9M\odot
have a higher probability to host a native BH, but their occupation fraction
decreases below 10%.
