The Evolution of Black Hole Mass and Spin in Active Galactic Nuclei
  We argue that supermassive black hole growth in AGN occurs via sequences of randomly--oriented accretion discs with angular momentum limited by self--gravity. These stably co-- or counter--align with the black hole spin with almost equal frequency. Accretion from these discs very rapidly adjusts the hole's spin parameter to average values $\bar a \sim 0.1-0.3$ (the precise range depending slightly on the disc vertical viscosity coefficient $\alpha_2$) from any initial conditions, but with significant fluctuations ($\Delta a\sim \pm 0.2$) about these. We conclude (a) AGN black holes should on average spin moderately, with the mean value $\bar a$ decreasing slowly as the mass increases; (b) SMBH coalescences leave little long--term effect on $\bar a$; (c) SMBH coalescence products in general have modest recoil velocities, so that there is little likelihood of their being ejected from the host galaxy; (d) black holes can grow even from stellar masses to $\sim 5\times 10^9 \msun$ at high redshift $z\sim 6$; (e) jets produced in successive accretion episodes can have similar directions, but after several episodes the jet direction deviates significantly. Rare examples of massive holes with larger spin parameters could result from prograde coalescences with SMBH of similar mass, and are most likely to be found in giant ellipticals. We compare these results with observation.   (abridged) 
A.R. King, J.E. Pringle, J.A. Hofmann