  The centers of stellar spheroids are often marked by the presence of
nucleated central regions, called nuclear star clusters (NSCs). The origin of
NSCs is still unclear. Here we investigate the possibility that NSCs originate
from the migration and merger of stellar clusters at the center of galaxies
where a massive black hole (MBH) may sit. We show that the observed relation
between NSC masses and the velocity dispersion of their host spheroids cannot
be reconciled with a purely in-situ formation scenario. On the other hand, the
observed relation appears to be in agreement with the predictions of the
cluster merger model which also reproduces the observed relation between the
size of NSCs and their total luminosity. We evolve through dynamical friction a
population of stellar clusters in a model of a galactic bulge taking into
account dynamical dissolution, starting from a power-law cluster initial mass
function and a total mass in stellar clusters consistent with the cluster
formation efficiency of the Milky Way (MW). The most massive clusters reach the
center of the galaxy and merge to form a compact nucleus; after 10 Gyr, the
resulting NSC has properties that are consistent with the observed distribution
of stars in the MW NSC. When a MBH is included at the center of a galaxy,
globular clusters are tidally disrupted during inspiral, resulting in NSCs with
lower densities than those of NSCs forming in galaxies with no MBHs. We suggest
this as a possible explanation for the lack of NSCs in galaxies containing MBHs
more massive than ~10^8M_Sun. Finally, we investigate the orbital evolution of
globular clusters in giant elliptical galaxies which are believed to always
host a MBH at their center rather than a NSC. In these systems an additional
mechanism can prevent a NSC from forming: the time for globular clusters to
reach the center of the galaxy is much longer than the Hubble time.
