  We revisit the longstanding question of whether first brightest cluster
galaxies are statistically drawn from the same distribution as other cluster
galaxies or are "special", using the new non-parametric, empirically based
model presented in Vale&Ostriker (2006) for associating galaxy luminosity with
halo/subhalo masses. We introduce scatter in galaxy luminosity at fixed halo
mass into this model, building a conditional luminosity function (CLF) by
considering two possible models: a simple lognormal and a model based on the
distribution of concentration in haloes of a given mass. We show that this
model naturally allows an identification of halo/subhalo systems with groups
and clusters of galaxies, giving rise to a clear central/satellite galaxy
distinction.
  We then use these results to build up the dependence of brightest cluster
galaxy (BCG) magnitudes on cluster luminosity, focusing on two statistical
indicators, the dispersion in BCG magnitude and the magnitude difference
between first and second brightest galaxies. We compare our results with two
simple models for BCGs: a statistical hypothesis that the BCGs are drawn from a
universal distribution, and a cannibalism scenario merging two galaxies from
this distribution. The statistical model is known to fail from work as far back
as Tremaine&Richstone (1977). We show that neither the statistical model nor
the simplest possibility of cannibalism provide a good match for observations.
Our CLF models both give similar results, in good agreement with observations.
Specifically, we find <m_1> between -25 and -25.5 in the K-band,
sigma(m_1)~0.25 and <Delta_12> between 0.6 and 0.8, for cluster luminosities in
the range of 10^12 to 10^13 h^-2 L_sun.
