  Massive black holes (MBHs) in contrast to stellar mass black holes are
expected to substantially change their properties over their lifetime. MBH
masses increase by several order of magnitude over the Hubble time, as
illustrated by Soltan's argument. MBH spins also must evolve through the series
of accretion and mergers events that grow the MBH's masses. We present a simple
model that traces the joint evolution of MBH masses and spins across cosmic
time. Our model includes MBH-MBH mergers, merger-driven gas accretion,
stochastic fueling of MBHs through molecular cloud capture, and a basic
implementation of accretion of recycled gas. This approach aims at improving
the modeling of low-redshift MBHs and AGN, whose properties can be more easily
estimated observationally. Despite the simplicity of the model, it captures
well the global evolution of the MBH population from z\sim6 to today. Under our
assumptions, we find that the typical spin and radiative efficiency of MBHs
decrease with cosmic time because of the higher incidence of stochastic
processes in gas-rich galaxies and MBH-MBH mergers in gas-poor galaxies. At z=0
the spin distribution in gas-poor galaxies peaks at spins 0.4-0.8, and it is
not strongly mass dependent. MBHs in gas-rich galaxies have a more complex
evolution, with low-mass MBHs at low redshift having low spins, and spins
increasing at larger masses and redshifts. We also find that at z>1 MBH spins
are on average highest in high luminosity AGN, while at lower redshifts these
differences disappear.
