  This study explores the space density and properties of active galaxies to
z=0.8. We have investigated the frequency and nature of unresolved nuclei in
galaxies at moderate redshift as indicators of nuclear activity such as Active
Galactic Nuclei (AGN) or starbursts. Candidates are selected by fitting imaged
galaxies with multi-component models using maximum likelihood estimate
techniques to determine the best model fit. We select those galaxies requiring
an unresolved point-source component in the galaxy nucleus, in addition to a
disk and/or bulge component, to adequately model the galaxy light. We have
searched 70 WFPC2 images primarily from the Medium Deep Survey for galaxies
containing compact nuclei. In our survey of 1033 galaxies, the fraction
containing an unresolved nuclear component greater than 5% of the total galaxy
light is 9+/-1% corrected for incompleteness. In this second of two papers in
this series, we discuss the nature of the compact nuclei and their hosts.
  We present the upper limit luminosity function (LF) for low-luminosity AGN
(LLAGN) in two redshift bins to z=0.8. Mild number density evolution is
detected for nuclei at -18 < M_B < -14. The LFs appear to flatten at M_B > -16
and this flatness, combined with the increase in number density, is
inconsistent with pure luminosity evolution. Based on the amount of density
evolution observed for these objects, we find that almost all present-day
spiral galaxies could have hosted a LLAGN at some point in their lives. We also
comment on the likely contribution of these compact nuclei to the soft X-ray
background.
