  We study the dynamics and evolution of the Milky Way nuclear star cluster
performing a high resolution direct one-million-body simulation. Focusing on
the interactions between such stellar system and the central supermassive black
hole, we find that different stellar components adapt their overall
distribution differently. After 5 Gyr, stellar mass black holes are
characterized by a spatial distribution with power-slope $-1.75$, fully
consistent with the prediction of Bahcall-Wolf pioneering work. Using the vast
amount of data available, we infer the rate for tidal disruption events, being
$4 \times 10^{-6}$ per yr, and estimate the number of objects that emit
gravitational waves during the phases preceding the accretion onto the
super-massive black hole, $\sim 270$ per Gyr. We show that some of these
sources could form extreme mass-ratio inspirals. We follow the evolution of
binary stars population, showing that the initial binary fraction of $5\%$
drops down to $2.5\%$ inside the inner parsec. Also, we explored the possible
formation of binary systems containing a compact object, discussing the
implications for millisecond pulsars formation and the development of Ia
Supernovae.
