The ordering process of asymmetric PS-b-PMMA block copolymers (BCPs) is investigated on flat SiO2 surfaces and on topographically patterned substrates. The topographic patterns consist of periodic gratings of 10 trenches defined by conventional top-down approaches and subsequently neutralized using a P(S-r-MMA) random copolymer (RCP). When the ordering process is accomplished on a flat surface at a temperature ranging between 180 and 230 °C, cylindrical microdomains perpendicularly oriented with respect to the substrate are observed irrespective of annealing temperature. In contrast, when the ordering process occurs on topographically patterned substrates, different phenomena have to be considered. The simultaneous effect of the flow around the gratings and the BCP flux from the zone located between adjacent trenches (mesa) into the inner part of the trenches results in significant thickness …