  We study the origin and properties of 'extra' or 'excess' central light in
the surface brightness profiles of gas-rich merger remnants. Combining a large
set of hydrodynamical simulations with data on observed mergers (spanning a
broad range of profiles at various masses and degrees of relaxation), we show
how to robustly separate the physically meaningful extra light -- stellar
populations formed in a compact central starburst during a gas-rich merger --
from the outer profile established by violent relaxation acting on stars
already present in the progenitors prior to the final merger. This separation
is sensitive to the profile treatment, and we demonstrate that certain fitting
procedures can yield physically misleading results. We show that our method
reliably recovers the younger starburst population, and examine how the
properties of this component scale with mass, gas content, and other aspects of
the progenitors. We consider the time evolution of profiles in different bands,
and estimate biases introduced by observational studies at different times and
wavelengths. We show that extra light is ubiquitous in observed and simulated
gas-rich merger remnants, with sufficient mass (~3-30% of the stellar mass) to
explain the discrepancy in the maximum phase-space densities of ellipticals and
their progenitor spirals. The nature of this central component provides
powerful new constraints on the formation histories of observed systems.
