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 $M_{500,c}=2times10^{13}-10^{15}$ 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 $M_starpropto M_{500,c}^{0.48pm0.06}$. Fixing the exponent of this power law for all redshifts, we constrain the normalization of this relation to be $2.08pm0.21$ 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.
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