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In many galactic nuclei, a nuclear stellar cluster (NSC) co-exists with asupermassive black hole (SMBH). In this work, we explore the idea that the NSCforms before the SMBH through the merger of several stellar clusters that maycontain intermediate-mass black holes (IMBHs). These IMBHs can subsequentlygrow by mergers and accretion to form an SMBH. To check the observableconsequences of this proposed SMBH seeding mechanism, we created anobservationally motivated mock population of galaxies, in which NSCs areconstructed by aggregating stellar clusters that may or may not contain IMBHs.We model the growth of IMBHs in the NSCs through gravitational wave (GW)mergers with other IMBHs and gas accretion. In the case of GW mergers, themerged BH can either be retained or ejected depending on the GW recoil kick itreceives. The likelihood of retaining the merged BH increases if we considergrowth of IMBHs in the NSC through gas accretion. We find that nucleatedlower-mass galaxies ($\rm M_{\star} \lesssim 10^{9} \ M_{\odot}$; e.g. M33)have an SMBH seed occupation fraction of about 0.3 to 0.5. This occupationfraction increases with galaxy stellar mass and for more massive galaxies ($\rm10^{9} \ M_{\odot} \lesssim \rm M_{\star} \lesssim 10^{11} \ M_{\odot}$), it isbetween 0.5 and 0.8, depending on how BH growth is modelled. These occupationfractions are consistent with observational constraints. Furthermore, allowingfor BH growth also allows us to reproduce the observed diversity in the massrange of SMBHs in the $\rm M_{\rm NSC} - M_{\rm BH}$ plane.

Formation of supermassive black holes in galactic nuclei II: retention and growth of seed intermediate-mass black holes