The structuring of films based on regular six-arm and twelve-arm polystyrenes with the arm characteristics Mn = 118 × 103 and Mw/Mn = 1.06 and a fullerene (С60) branching center in a weakly swollen state in a mixture of deuterated solvents (90 vol % D-methanol and 10 vol % D-toluene) is studied by small-angle neutron scattering. Analogous studies are performed for films based on linear polystyrene (Mn = 280 × 103, Mw/Mn = 1.07) and its composites with fullerene С60 (0.5 wt %). It is shown that, during saturation of the samples with the solvent D-toluene, filling of the free volume that forms chain-transport channels that have gyration radii of the order of diameters of macromolecules and unite to form submicron and micron structures occurs. The degree of filling of the free volume, which is maximum for the linear polymer, becomes minimum for polystyrene with the inserted free fullerene. In addition, the transition from the linear polymer to the six-arm polymer is related to a smaller degree of filling of the free volume due to the formation of thinner migration channels. As the amount of arms in macromolecules is increased to 12, permeability of the polymer matrix improves because molecular order partially appears in accordance with the model of the densest packing of solid spheres.