  Based on a high resolution cosmological n-body simulation, we track the
hierarchical growth of black holes in galaxy clusters from z=20 to z=0. We
present a census of black holes as function of redshift and will determine
their mass assembly history under a variety of assumptions regarding the
importance of gas accretion in black hole growth, from early supercritical
Eddington accretion to gas-poor hierarchical assembly. Following a galaxy
merger, black holes are expected to form, inspiral and merge after strongly
radiating energy via gravitational waves. For each binary black hole inspiral
and merger, we determine the expected gravitational wave signal for the Laser
Interferometer Space Antenna (LISA), and calculate the LISA event rate as a
function of time. We will calculate the black hole mass assembly history for
several black hole growth scenerios, so that we can explore tests to
characterize each model observationally. In particular, we will study how well
LISA observations will be able to distinguish between these very different
assembly scenarios.
