  We determine the distribution of free ends and the monomer insertion
potential in the strongly-stretched limit for regularly and statistically
branched polymer brushes. We find that the end density flattens in the limit of
very strong branching with a concomitant enhancement of the grafting surface
end density. This enhancement ensures for a wide range of parameters that a
parabolic potential profile is preserved, even for large positive curvature of
the brush surface. This considerably simplifies the analysis of copolymer
phases.
