  In this article we consider the growth of seed black holes immersed in dark
matter halos. We first investigate the adiabatic growth in various initial
distribution functions (isothermal, power law, and NFW) and find the resulting
density, radial velocity, and anisotropy profiles. In addition we estimate the
growth rate for a given black hole mass in the corresponding adiabatically
modified dark matter distribution function. Only in the isothermal case is
there a convincing black hole mass-age relation. By calculating the line of
sight velocity dispersion for the various cases as a function of the black hole
mass, we find the predicted adiabatic $M_{bh}-\sigma$ relation; this never
approaches the recently observed power law. We conclude by abandoning
adiabaticity, suggesting that the black hole grows proportionally to the dark
matter halo itself on a dynamic time scale. This allows us to relate the
observed $M_{bh}-\sigma$ relation to the cosmological power spectrum on
galactic scales by using dimensional scaling arguments.
