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We assess models for the assembly of supermassive black holes (SMBHs) at thecenter of galaxies that trace their hierarchical build-up far up in the darkhalo `merger tree'. We assume that the first `seed' black holes (BHs) formed in(mini)halos collapsing at z=20 from high-sigma density fluctuations. As thesepregalactic holes become incorporated through a series of mergers into largerand larger halos, they sink to the center owing to dynamical friction, accretea fraction of the gas in the merger remnant to become supermassive, form abinary system, and eventually coalesce. The merger history of dark matter halosand associated BHs is followed by cosmological Monte Carlo realizations of themerger hierarchy. A simple model, where quasar activity is driven by majormergers and SMBHs accrete at the Eddington rate a mass that scales with thefifth power of the velocity dispersion, is shown to reproduce the optical LF ofquasars in the redshift range 1<z<4. Binary and triple BH interactions arefollowed in our merger tree. The assumptions underlying our scenario lead tothe prediction of a population of massive BHs wandering in galaxy halos and theintergalactic medium at the present epoch, and contributing <10% to the totalBH mass density. At all epochs the fraction of binary SMBHs in galaxy nuclei isof order 10%, while the fraction of binary quasars is less than 0.3%Comment: revised version, accepted for publication in the ApJ, emulateapj, 15  pages, 16 figure

The Assembly and Merging History of Supermassive Black Holes in Hierarchical Models of Galaxy Formation