  We used the HST WFPC2 to obtain I-band images of the centers of 81 brightest
cluster galaxies (BCGs), drawn from a volume-limited sample of nearby BCGs. The
images show a rich variety of morphological features, including multiple or
double nuclei, dust, stellar disks, point source nuclei, and central surface
brightness depressions. High resolution surface brightness profiles could be
inferred for 60 galaxies. Of those, 88% have well-resolved cores. Twelve
percent of the BCG sample lacks a well-resolved core; all but one of these BCGs
have ``power-law'' profiles. Some of these galaxies have higher luminosities
than any power-law galaxy identified by Faber et al. (1997), and have physical
upper limits on the break radius well below the values observed for core
galaxies of the same luminosity. These results support the idea that the
central structure of early-type galaxies is bimodal in its physical properties,
but also suggest that there exist high luminosity galaxies with power-law
profiles (or unusually small cores). The BCGs in the latter category tend to
fall at the low end of the BCG luminosity function and tend to have low values
of the quantity alpha (the logarithmic slope of the metric luminosity as a
function of radius, at 10 kpc). Since theoretical calculations have shown that
the luminosities and alpha values of BCGs grow with time as a result of
accretion, this suggests a scenario in which elliptical galaxies evolve from
power-law profiles to core profiles through accretion and merging. This is
consistent with theoretical scenarios that invoke the formation of massive
black hole binaries during merger events (Abridged).
