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.
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