We report the effect of increasing amounts of glycidyl methacrylate (GMA) in random copolymers of P(S-r-MMA-r-GMA) on the formation of nonpreferential mats for the assembly of P(S-b-MMA) block copolymers. Increasing the GMA concentration in the random copolymer from 1 (PG1) to 4 (PG4) mole % increased the cross-linking efficiency and reduced the effective minimum thickness of the cross-linked mat for perpendicular alignment of P(S-b-MMA) from similar to 6 nm to similar to 2 nm. The compositional window (so-called perpendicular window) of PG4 was defined for both symmetric and asymmetric P(S-b-MMA). Compared to PG1, incorporation of higher amount of polar comonomer (GMA) in PG4 shifted the perpendicular window toward higher styrene fraction as a result of the increased polarity. The defined perpendicular window for P(S-r-MMA-r-GMA) is equally applicable for random copolymers prepared by both controlled living and classical free-radical polymerizations.