The self-assembly of a lamella-forming blend of a diblock copolymer and its respective homopolymers on periodically patterned substrates is investigated by a concerted experimental and theoretical approach. The substrate pattern consists of square arrays of spots that preferentially attract one component of the blend. The mismatch between the lamellar equilibrium morphology of the copolymer material and the substrate pattern results in the formation of a bicontinuous morphology. At the substrate, a quadratically perforated lamella (QPL) assembles in perfect registry with the substrate pattern. From this, QPL necks emanate and reach the top surface of the film. The detailed structure of these cylindrical nanochannels is analyzed using Voronoi tessellation, orientation correlation functions, and the structure factor of the neck positions on the top surface. The surface morphology is dictated by the antagonism of the square symmetry of the substrate pattern and the tendency of the necks to locally pack in a hexagonal arrangement. The analogy and differences to a system of adsorbed monolayer on corrugated substrates is explored by comparing the arrangement of the necks on the film's top surface with the structure of a soft disk model on a quadratically corrugated substrate. (c) 2006 Wiley Periodicals, Inc.