  Nuclear stellar cluster (NSCs) are known to exist around massive black holes
(MBHs) in galactic nuclei. Two formation scenarios were suggested for their
origin: Build-up of NSCs and Continuous in-situ star-formation. Here we 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 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. However, its
younger stellar population do not yet achieve a steady state. In
particular,formed/evolved NSCs with in-situ star-formation contain differential
age-segregated stellar populations which are not yet fully mixed. Younger
stellar populations formed in the outer regions of the NSC have a cuspy
structure towards the NSC outskirts, while showing a core-like distribution
inwards; with younger populations having larger core sizes.
