  We consider black hole - galaxy coevolution using simple analytic arguments.
We focus on the fact that several supermassive black holes are known with
masses significantly larger than suggested by the $M - {\sigma}$ relation,
sometimes also with rather small stellar masses. We show that these are likely
to have descended from extremely compact `blue nugget' galaxies born at high
redshift, whose very high velocity dispersions allowed the black holes to reach
unusually large masses. Subsequent interactions reduce the velocity dispersion,
so the black holes lie above the usual $M - {\sigma}$ relation and expel a
large fraction of the bulge gas (as in WISE J104222.11+164115.3) that would
otherwise make stars, before ending at low redshift as very massive holes in
galaxies with relatively low stellar masses, such as NGC 4889 and NGC 1600. We
further suggest the possible existence of two new types of galaxy: low-mass
dwarfs whose central black holes lie below the $M - {\sigma}$ relation at low
redshift, and galaxies consisting of very massive ($\gtrsim
10^{11}$M$_{\odot}$) black holes with extremely small stellar masses. This
second group would be very difficult to detect electromagnetically, but
potentially offer targets of considerable interest for LISA.
