  The origin of the population of very massive stars observed within $\sim 0.4$
pc of the supermassive black hole in the Galactic Centre is a mystery. Tidal
forces from the black hole would likely inhibit {\it in situ} star formation
whilst the youth of the massive stars would seem to exclude formation elsewhere
followed by transportation (somehow) into the Galactic centre. Here we consider
a third way to produce these massive stars from the lower-mass stars contained
in the nuclear stellar cluster which surrounds the supermassive black hole. A
passing gas cloud can be tidally shredded by the supermassive black hole
forming an accretion disc around the black hole. Stars embedded within this
accretion disc will accrete gas from the disc via Bondi-Hoyle accretion, where
the accretion rate onto a star, $\dot{M}_\star \propto M_\star^2$. This
super-exponential growth of accretion can lead to a steep increase in stellar
masses, reaching the required 40-50 M$_\odot$ in some cases. The mass growth
rate depends sensitively on the stellar orbital eccentricities and their
inclinations. The evolution of the orbital inclinations and/or their
eccentricities as stars are trapped by the disc, and their orbits are
circularised, will increase the number of massive stars produced. Thus
accretion onto low-mass stars can lead to a top heavy stellar mass function in
the Galactic Centre and other galactic nuclei. The massive stars produced will
pollute the environment via supernova explosions and potentially produce
compact binaries whose mergers may be detectable by the LIGO-VIRGO
gravitational waves observatories.
