The cylindrical domain diameter (d), spacing (D), and uniformity in thin films of ternary blends of a cylinder-forming polystyrene-block-poly(methyl methacrylate) block copolymer and the corresponding homopolymers were investigated as a function of the molecular weight (M-n) and concentration (phi(H)) of the homopolymers. Thin films (20-65 nm) of the blends were deposited on silicon wafers that had been modified with random copolymer brushes such that the cylindrical domains of the annealed blends were oriented perpendicular to the substrate. The best uniformity of d, at a given phi(H) was achieved in the blends with lower homopolymer M(n)s. For blends made with homopolymers that had M-n values of the same order of magnitude as those of the corresponding blocks of the copolymer, D increased with increasing phi(H) as D = D-0(1 - phi(H))(-beta), where D-0 is the domain spacing of the block copolymer and beta is a parameter that depends on the ratio of the homopolymer and block copolymer molecular weights. The cylindrical domains of the blends could be swollen up to 150% of the original diameter while maintaining hexagonal ordering. For most of the blends on the random copolymer brushes, uniform arrays of perpendicular cylinders were formed most frequently at a film thickness near D-0. A ternary blend with homopolymers with very low M(n)s produced markedly different results: D decreased in size with increasing phi(H), measurable up to phi(H) = 0.4, and produced uniform patterns in films with thicknesses ranging from 20 to 37 nm.