Dynamics of galactic nuclei: mass segregation and collisions

Massive black holes (MBHs) with a mass below ~ 10⁷ M_⊙ are likely to reside at the centre of dense stellar nuclei shaped by 2-body relaxation, close interactions with the MBH and direct collisions. In this contribution, we stress the role of mass segregation of stellar-mass black holes into the innermost tenths of a parsec and point to the importance of hydrodynamical collisions between stars. At the Galactic centre, collisions must affect giant stars and some of the S-stars.