  We examine the central-galaxy luminosity -- host-halo mass relation for 54
Brightest Group Galaxies (BGGs) and 92 Brightest Cluster Galaxies (BCGs) at
z<0.1 and present the first measurement of this relation for a sample of known
BCGs at 0.1<z<0.8 (average z~0.3). At z<0.1 we find L_K \propto
M_{200}^{0.24\pm0.08} for the BCGs and the early-type BGGs in groups with
extended X-ray emission and L_K \propto M_{200}^{0.11\pm0.10} for the BCGs
alone. At 0.1<z<0.8 we find L_K \propto M_{200}^{0.28\pm0.11}. We conclude that
there is no evidence for evolution in this relationship between z<0.1 and
z<0.8: BCG growth appears to still be limited by the timescale for dynamical
friction at these earlier times, not proceeding according to the predictions of
current semi-analytic models.
