We use Hubble Space Telescope archival images to measure central surface brightness profiles of globular clusters around satellite galaxies of the Milky Way. We report results for 21 clusters around the LMC, 5 around the SMC, and 4 around the Fornax dwarf galaxy. The profiles are obtained using a recently developed technique based on measuring integrated light, which is tested on an extensive simulated dataset. Our results show that for 70% of the sample, the central photometric points of our profiles are brighter than previous measurements using star counts with deviations as large as 2 mag/arcsec^2. About 40% of the objects have central profiles deviating from a flat central core, with central logarithmic slopes continuously distributed between -0.2 and -1.2. These results are compared with those found for a sample of Galactic clusters using the same method. We confirm the known correlation in which younger clusters tend to have smaller core radii, and we find that they also have brighter central surface brightness values. This seems to indicate that globular clusters might be born relatively concentrated, and that a profile with extended flat cores might not be the ideal choice for initial profiles in theoretical models.
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