  Studying how nuclear star clusters (NSCs) form and how they are related to
the growth of the central massive black holes (MBHs) and their host galaxies is
fundamental for our understanding of the evolution of galaxies and the
processes that have shaped their central structures. We present the results of
a semi-analytical galaxy formation model that follows the evolution of dark
matter halos along merger trees, as well as that of the baryonic components.
This model allows us to study the evolution of NSCs in a cosmological context,
by taking into account the growth of NSCs due to both dynamical friction-driven
migration of stellar clusters and star formation triggered by infalling gas,
while also accounting for dynamical heating from (binary) MBHs. We find that
in-situ star formation contributes a significant fraction (up to ~80%) of the
total mass of NSCs in our model. Both NSC growth through in-situ star formation
and through star cluster migration are found to generate NSC -- host galaxy
scaling correlations that are shallower than the same correlations for MBHs. We
explore the role of galaxy mergers on the evolution of NSCs, and show that
observational data on NSC -- host galaxy scaling relations provide evidence of
partial erosion of NSCs by MBH binaries in luminous galaxies. We show that this
observational feature is reproduced by our models, and we make predictions
about the NSC and MBH occupation fraction in galaxies. We conclude by
discussing several implications for theories of NSC formation.
