  We analyze Hubble Space Telescope surface-brightness profiles of 61
elliptical galaxies and spiral bulges (hot galaxies). Luminous hot galaxies
have cuspy cores with steep outer power-law profiles that break at r ~ r_b to
shallow inner profiles with logslope less than 0.3. Faint hot galaxies show
steep, largely featureless power-law profiles at all radii and lack cores. The
centers of power-law galaxies are up to 1000 times denser in mass and
luminosity than the cores of large galaxies at a limiting radius of 10 pc. At
intermediate magnitudes (-22.0 < M_V < -20.5), core and power-law galaxies
coexist, and there is a range in r_b at a given luminosity of at least two
orders of magnitude. Central properties correlate with global rotation and
shape: core galaxies tend to be boxy and slowly rotating, whereas power-law
galaxies tend to be disky and rapidly rotating. The dense power-law centers of
disky, rotating galaxies are consistent with their formation in gas-rich
mergers. The parallel proposition that cores are simply the by-products of
gas-free stellar mergers is less compelling. For example, core galaxies accrete
small, dense, gas-free galaxies at a rate sufficient to fill in low-density
cores if the satellites survived and sank to the center. An alternative model
for core formation involves the orbital decay of massive black holes (BHs): the
BH may heat and eject stars from the center, eroding a power law if any exists
and scouring out a core. An average BH mass per spheroid of 0.002 times the
stellar mass yields reasonably good agreement with the masses and radii of
observed cores and in addition is consistent with the energetics of AGNs and
kinematic detections of BHs in nearby galaxies.
