  We reanalyze the galaxy-mass correlation function measured by the Sloan
Digital Sky Survey to obtain host dark matter halo masses at galaxy and galaxy
group scales. We extend the data to galaxy clusters in the 2MASS catalog and
study the relation between central galaxy luminosity and halo mass. While the
central galaxy luminosity scales as ~M^{0.7-0.8} at low masses, the relation
flattens to ~M^{<0.3} above ~4x10^{13} M_sun. The total luminosity of galaxies
in the halo, however, continues to grow as a power-law ~M^{0.8-0.9}. Starting
from the hypothesis that the central galaxies grow by merging ("galactic
cannibalism"), we develop a simple model for the evolution of their
luminosities as a consequence of the accretion of satellite galaxies. The
luminosity-mass relation flattens when the time scale on which dynamical
friction induces orbital decay in the satellite galaxies exceeds the age of the
dark matter halo. Then, the growth of the central galaxy is suppressed as it
can cannibalize only the rare, massive satellite galaxies. The model takes the
dependence of the total luminosity of galaxies in a halo on its mass and the
global galaxy luminosity function as input, and reproduces the observed central
galaxy luminosity-mass relation over three decades in halo mass,
(10^{12}-10^{15}) M_sun.
  The success of the model suggests that gas cooling and subsequent star
formation did not play an important role in the final assembly of central
galaxies from sub-L_star precursors.
