| Abstract: | Nuclear stellar cluster (NSCs) are known to exist around massive black holes (MBHs) in galactic nuclei. Two formation scenarios were suggested for their origin: (1) Build-up of NSCs from consecutive infall of stellar cluster and (2) Continuous in-situ star-formation following gas inflow into the galaxy nucleus. Though the cluster-infall scenario has been extensively studied in recent years, the in-situ formation, and in particular the role of star-formation in the long-term build-up of NSCs and their evolution have been hardly studied. Here we use Fokker-Planck calculations to study the effects of star formation on the build-up of NSCs and its implications for their long term evolution and their resulting structure. We use the Fokker-Planck equation to describe the evolution of several stellar populations, and add appropriate source terms to account for the effects of newly formed stars. We show that continuous star-formation can lead to the build-up of an NSC with properties similar to those of the Milky-way NSC. We also find that the general structure of the old stellar population in the NSC with in-situ star-formation could be very similar to the steady-state Bahcall-Wolf cuspy structure. Moreover, we notice a different behavior in the density of stellar populations composed of stars with different mass and age (age and mass segregation). In addition, we study the dependence of stars tidal disruption events (TDEs) on the type of galaxy, as well as the dependence on the MBH mass, and give a prediction of the TDEs history in different models of NSCs. Finally we estimate inspiral rates of compact objects into MBHs, a process which emits gravitational waves. |