Equilibrium distributions of polymer chain segments in solution near an impenetrable, but otherwise noninteracting, plane barrier are studied for random-flight regular star species comprising identical linear subchains joined at a common node. Although the polymer concentration in the diffuse depletion layer created by entropic repulsion of chains from the barrier vanishes at the wall, segments in different positions in the chains are not distributed identically. Chain ends are favored over interior segments near the wall, and branch nodes experience the greatest repulsion. Calculations of segment density versus distance profiles for any given position in the chain and the overall averaged density profile require single and double numerical integration, respectively, but certain analytic properties of the profiles can be derived. Correlation with the mean projection of the polymer molecule on a line is of particular interest since this quantity is a measure of the mean thickness of the depletion layer for any molecular model without molecular interactions.