  We study the origin and properties of 'extra' or 'excess' central light in
the surface brightness profiles of cusp or power-law ellipticals. Dissipational
mergers give rise to two-component profiles: an outer profile established by
violent relaxation acting on stars present in the progenitors prior to the
final merger, and an inner stellar population comprising the extra light,
formed in a compact starburst. Combining a large set of hydrodynamical
simulations with data that span a broad range of profiles and masses, we show
that this picture is borne out -- cusp ellipticals are indeed 'extra light'
ellipticals -- and examine how the properties of this component scale with
global galaxy properties. We show how to robustly separate the 'extra' light,
and demonstrate that observed cusps are reliable tracers of the degree of
dissipation in the spheroid-forming merger. We show that the typical degree of
dissipation is a strong function of stellar mass, tracing observed disk gas
fractions at each mass. We demonstrate a correlation between extra light
content and effective radius at fixed mass: systems with more dissipation are
more compact. The outer shape of the light profile does not depend on mass,
with a mean outer Sersic index ~2.5. We explore how this relates to shapes,
kinematics, and stellar population gradients. Simulations with the gas content
needed to match observed profiles also reproduce observed age, metallicity, and
color gradients, and we show how these can be used as tracers of the degree of
dissipation in spheroid formation.
