  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.
