  It is now well established that many galaxies have nuclear star clusters
(NCs) whose total masses correlate with the velocity dispersion (sigma) of the
galaxy spheroid in a very similar way to the well--known supermassive black
hole (SMBH) M - sigma relation. Previous theoretical work suggested that both
correlations can be explained by a momentum feedback argument. Observations
further show that most known NCs have masses < 10^8 Msun, while SMBHs
frequently have masses > 10^8 Msun, which remained unexplained in previous
work. We suggest here that this changeover reflects a competition between the
SMBH and nuclear clusters in the feedback they produce. When one of the massive
objects reaches its limiting M-sigma value, it drives the gas away and hence
cuts off its own mass and also the mass of the ``competitor''. The latter is
then underweight with respect to the expected M-sigma mass (abridged).
