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.

19 pages, 20 figures, submitted to MNRAS