We study the radial number density and stellar mass density distributions of satellite galaxies in a sample of 60 massive clusters at 0.04<z<0.26 selected from the Multi-Epoch Nearby Cluster Survey (MENeaCS) and the Canadian Cluster Comparison Project (CCCP). In addition to ~10,000 spectroscopically confirmed member galaxies, we use deep ugri-band imaging to estimate photometric redshifts and stellar masses, and then statistically subtract fore-, and background sources using data from the COSMOS survey. We measure the galaxy number density and stellar mass density distributions in logarithmically spaced bins over 2 orders of magnitude in radial distance from the BCGs. For projected distances in the range 0.1<R/R200<2.0, we find that the stellar mass distribution is well-described by an NFW profile with a concentration of c=2.03+/-0.20. However, at smaller radii we measure a significant excess in the stellar mass in satellite galaxies of about $10^{11}$ Msun per cluster, compared to these NFW profiles. We do obtain good fits to generalized NFW profiles with free inner slopes, and to Einasto profiles. To examine how clusters assemble their stellar mass component over cosmic time, we compare this local sample to the GCLASS cluster sample at z~1, which represents the approximate progenitor sample of the low-z clusters. This allows for a direct comparison, which suggests that the central parts (R<0.4 Mpc) of the stellar mass distributions of satellites in local galaxy clusters are already in place at z~1, and contain sufficient excess material for further BCG growth. Evolving towards z=0, clusters appear to assemble their stellar mass primarily onto the outskirts, making them grow in an inside-out fashion.
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