We discuss the link between dark matter halos hosting the first PopIII starsand the rare, massive, halos that are generally considered to host brightquasars at high redshift z~6. The main question that we intend to answer iswhether the super-massive black holes powering these QSOs grew out from theseeds planted by the first intermediate massive black holes created in theuniverse. This question involves a dynamical range of 10^13 in mass and weaddress it by combining N-body simulations of structure formation to identifythe most massive halos at z~6 with a Monte Carlo method based on linear theoryto obtain the location and formation times of the first light halos within thewhole simulation box. We show that the descendants of the first ~10^6 Msunvirialized halos do not, on average, end up in the most massive halos at z~6,but rather live in a large variety of environments. The oldest PopIIIprogenitors of the most massive halos at z~6, form instead from density peaksthat are on average one and a half standard deviations more common than thefirst PopIII star formed in the volume occupied by one bright high-z QSO. Theintermediate mass black hole seeds planted by the very first PopIII stars atz>40 can easily grow to masses m_BH>10^9.5 Msun by z=6 assuming Eddingtonaccretion with radiative efficiency \epsilon~0.1. Quenching of the black holeaccretion is therefore crucial to avoid an overabundance of supermassive blackholes at lower redshift. This can be obtained if the mass accretion is limitedto a fraction \eta~6*10^{-3} of the total baryon mass of the halo hosting theblack hole. The resulting high end slope of the black hole mass function at z=6is \alpha ~ -3.7, a value within the 1\sigma error bar for the bright end slopeof the observed quasar luminosity function at z=6.
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