The Assembly and Merging History of Supermassive Black Holes in   Hierarchical Models of Galaxy Formation
  We assess models for the assembly of supermassive black holes (SMBHs) at the center of galaxies that trace their hierarchical build-up far up in the dark halo `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 these pregalactic holes become incorporated through a series of mergers into larger and larger halos, they sink to the center owing to dynamical friction, accrete a fraction of the gas in the merger remnant to become supermassive, form a binary system, and eventually coalesce. The merger history of dark matter halos and associated BHs is followed by cosmological Monte Carlo realizations of the merger hierarchy. A simple model, where quasar activity is driven by major mergers and SMBHs accrete at the Eddington rate a mass that scales with the fifth power of the velocity dispersion, is shown to reproduce the optical LF of quasars in the redshift range 1<z<4. Binary and triple BH interactions are followed in our merger tree. The assumptions underlying our scenario lead to the prediction of a population of massive BHs wandering in galaxy halos and the intergalactic medium at the present epoch, and contributing <10% to the total BH mass density. At all epochs the fraction of binary SMBHs in galaxy nuclei is of order 10%, while the fraction of binary quasars is less than 0.3% 
Marta Volonteri, Francesco Haardt, & Piero Madau