From galactic nuclei to the halo outskirts: tracing supermassive black holes across cosmic history and environments

We study the mass assembly and spin evolution of supermassive black holes (BHs) across cosmic time as well as the impact of gravitational recoil on the population of nuclear and wandering black holes (wBHs) by using the semi-analytical model LGalaxies run on top of Millennium merger trees. We track spin changes that BHs experience during both coalescence events and gas accretion phases. For the latter, we assume that spin changes are coupled with the bulge assembly. This assumption leads to predictions for the median spin values of z=0 BHs that depend on whether they are hosted by pseudobulges, classical bulges or ellipticals, being a ~ 0.9, 0.7 and 0.4, respectively. The outcomes of the model display a good consistency with z 10^{13} M_{\odot} and M_{stellar}>10^{10} M_{\odot}, being orphan wBHs the dominant type. Besides, independently of redshift and halo mass, \textit{ejected} wBHs inhabit the central regions ( 0.5R_{200}). Finally, we find that gravitational recoils cause a progressive depletion of nuclear BHs with decreasing redshift and stellar mass. Moreover, ejection events lead to changes in the predicted local black hole-bulge relation, in particular for BHs in pseudobulges, for which the relation is flattened at M_{bulge}>10^{10.2} M{\odot} and the scatter increase up to ~3dex.