  We constrain the evolution of the brightest cluster galaxy plus intracluster
light (BCG+ICL) using an ensemble of 42 galaxy groups and clusters that span
redshifts of z = 0.05-1.75 and masses of $M_{500,c}=2\times10^{13}-10^{15}$
M$_\odot$ Specifically, we measure the relationship between the BCG+ICL stellar
mass $M_\star$ and $M_{500,c}$ at projected radii 10 < r < 100 kpc for three
different epochs. At intermediate redshift (z = 0.40), where we have the best
data, we find $M_\star\propto M_{500,c}^{0.48\pm0.06}$. Fixing the exponent of
this power law for all redshifts, we constrain the normalization of this
relation to be $2.08\pm0.21$ times higher at z = 0.40 than at high redshift (z
= 1.55). We find no change in the relation from intermediate to low redshift (z
= 0.10). In other words, for fixed $M_{500,c}$, $M_\star$ at 10 < r < 100 kpc
increases from z = 1.55 to z = 0.40 and not significantly thereafter.
Theoretical models predict that the physical mass growth of the cluster from z
= 1.5 to z = 0 within $r_{500,c}$ is a factor of 1.4, excluding evolution due
to definition of $r_{500,c}$. We find that $M_\star$ within the central 100 kpc
increases by a factor of 3.8 over the same period. Thus, the growth of
$M_\star$ in this central region is more than a factor of two greater than the
physical mass growth of the cluster as a whole. Furthermore, the concentration
of the BCG+ICL stellar mass, defined by the ratio of stellar mass within 10 kpc
to the total stellar mass within 100 kpc, decreases with increasing $M_{500,c}$
at all redshift. We interpret this result as evidence for inside-out growth of
the BCG+ICL over the past ten Gyrs, with stellar mass assembly occuring at
larger radii at later times.
