  Current stellar evolution models predict a dearth of black holes (BHs) with
masses $\gtrsim 50$ M$_\odot$ and $\lesssim 5$ M$_\odot$, and intermediate-mass
black holes (IMBHs; $\sim10^2- 10^5$ M$_\odot$) have not yet been detected
beyond any reasonable doubt. A natural way to form massive BHs is through
repeated mergers, detectable via gravitational wave emission with current
LIGO/Virgo or future LISA and ET observations. Nuclear star clusters (NSCs)
have masses and densities high enough to retain most of the merger products,
which acquire a recoil kick at the moment of merger. We explore the possibility
that IMBHs may be born as a result of repeated mergers in NSCs, and show how
their formation pathways depend on the NSC mass and density, and BH spin
distribution. We find that BHs in the pair-instability mass gap can be formed
and observed by LIGO/Virgo, and show that the typical mass of the ejected
massive BHs is $400$--$500$ M$_\odot$, with velocities of up to a few thousand
km s$^{-1}$. Eventually some of these IMBHs can become the seeds of
supermassive BHs, observed today in the centers of galaxies. In dwarf galaxies,
they could potentially solve the abundance, core-cusp, too-big-to-fail,
ultra-faint, and baryon-fraction issues via plausible feedback scenarios.
