  Most stellar evolution models predict that black holes (BHs) should not exist
above approximately $50-70$ M$_\odot$, the lower limit of the pair-instability
mass gap. However, recent LIGO/Virgo detections indicate the existence of BHs
with masses at and above this threshold. We suggest that massive BHs, including
intermediate mass black holes (IMBHs), can form in galactic nuclei through
collisions between stellar-mass black holes and the surrounding main-sequence
stars. Considering dynamical processes such as collisions, mass segregation,
and relaxation, we find that this channel can be quite efficient, forming IMBHs
as massive as $10^4$ M$_\odot$. This upper limit assumes that (1) the BHs
accrete a substantial fraction of the stellar mass captured during each
collision and (2) that the rate at which new stars are introduced into the
region near the SMBH is high enough to offset depletion by stellar disruptions
and star-star collisions. We discuss deviations from these key assumptions in
the text. Our results suggest that BHs in the pair-instability mass gap and
IMBHs may be ubiquitous in galactic centers. This formation channel has
implications for observations. Collisions between stars and BHs can produce
electromagnetic signatures, for example, from x-ray binaries and tidal
disruption events. Additionally, formed through this channel, both black holes
in the mass gap and IMBHs can merge with the supermassive black hole at the
center of a galactic nucleus through gravitational waves. These gravitational
wave events are extreme and intermediate mass ratio inspirals (EMRIs and IMRIs,
respectively).
