All the physical processes involved in the formation, merging, and accretion history of massive black holes along the hierarchical build--up of cosmic structures are likely to leave an imprint on the gravitational waves detectable by future space--borne missions, such as LISA. We report here the results of recent studies, carried out by means of dedicated simulations of black hole build--up, aiming at understanding the impact on LISA observations of two ingredients that are crucial in every massive black hole formation scenario, namely: (i) the nature and abundance of the first black hole seeds and (ii) the large gravitational recoils following the merger of highly spinning black holes. We predict LISA detection rates spanning two order of magnitude, in the range 3-300 events per year, depending on the detail of the assumed massive black hole seed model. On the other hand, large recoil velocities do not dramatically compromise the efficiency of LISA observations. The number of detections may drop substantially (by ~60%), in scenarios characterized byabundant light seeds, but if seeds are already massive and/or relatively rare, the detection rate is basically unaffected.
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