  Nuclear Star Clusters (NSCs) are often present in spiral galaxies as well as
resolved Stellar Nuclei (SNi) in elliptical galaxies centres. Ever growing
observational data indicate the existence of correlations between the
properties of these very dense central star aggregates and those of host
galaxies, which constitute a significant constraint for the validity of
theoretical models of their origin and formation. In the framework of the well
known 'migratory and merger' model for NSC and SN formation, in this paper we
obtain, first, by a simple argument the expected scaling of the NSC/SN mass
with both time and parent galaxy velocity dispersion in the case of dynamical
friction as dominant effect on the globular cluster system evolution. This
generalizes previous results by \cite{TrOsSp} and is in good agreement with
available observational data showing a shallow correlation between NSC/SN mass
and galactic bulge velocity dispersion. Moreover, we give statistical relevance
to predictions of this formation model, obtaining a set of parameters to
correlate with the galactic host parameters. We find that the correlations
between the masses of NSCs in the migratory model and the global properties of
the hosts reproduce quite well the observed correlations, supporting the
validity of the migratory-merger model. In particular, one important result is
the flattening or even decrease of the value of the NSC/SN mass obtained by the
merger model as function of the galaxy mass for high values of the galactic
mass, i.e. $\gtrsim 3\times 10^{11}$M$_\odot$, in agreement with some growing
observational evidence.
