  A significant fraction of the stellar population in the cusp around central
black holes of galaxies consists of compact remnants of evolved stars, such as
white dwarfs, neutron stars and stellar mass black holes. We estimate the rate
of capture of compact objects by massive central black holes, assuming most
spiral galaxies have a central black hole of modest mass ($\sim 10^6 \msun$),
and a cuspy spheroid. It is likely that the total capture rate is dominated by
nucleated spirals. We estimate the flux of gravitational wave radiation from
such coalescences, and the estimated detectable source count for proposed
space--based gravitational wave observatories such as LISA. About one event per
year should be detectable within $1 \, {\rm Gpc}$, given very conservative
estimates of the black hole masses and central galactic densities. We expect
$10^2$--$10^3$ detectable sources at lower frequencies ($10^{-4}$ Hz) ``en
route'' to capture. If stellar mass black holes are ubiquitous, the signal may
be dominated by stellar mass black holes coalescing with massive black holes.
The rate of white dwarf--white dwarf mergers in the cores of nucleated spirals
is estimated at $\sim10^{-6}$ per year per galaxy.
