  We model the effects of collisions and close encounters on the stellar
populations observed in the Milky Way nuclear stellar cluster (NSC). Our
analysis is based on $N$-body simulations in which the NSC forms by accretion
of massive stellar clusters around a supermassive black hole. We attach stellar
populations to our $N$-body particles and follow the evolution of their stars,
and the rate of collisions and close encounters. The most common encounters are
collisions between pairs of main-sequence stars, which lead to mergers:
destructive collisions between main-sequence stars and compact objects are
rare. We find that the effects of collisions on the stellar populations are
small for three reasons. First, our models possess a core which limits the
maximum stellar density. Secondly, the velocity dispersion in the NSC is
similar to the surface escape velocities of the stars, which minimises the
collision rate. Finally, whilst collisions between main-sequence stars destroy
bright giants by accelerating their evolution, they also create them by
accelerating the evolution of lower-mass stars. These two effects approximately
cancel out. We also investigate whether the G2 cloud could be a fuzzball: a
compact stellar core which has accreted a tenuous envelope in a close encounter
with a red giant. We conclude that fuzzballs with cores below $2\,M_\odot$ have
thermal times-scales too short to reproduce G2. A fuzzball with a black-hole
core could reproduce the surface properties of G2 but the production rate of
such objects in our model is low.
