We study the assembly of PMMA cylinder forming poly(styrene-block-methyl methacrylate) in three different geometries: planar surface, and chemically homogeneous and heterogeneous graphoepitaxy as a function of film thickness and surface chemical composition. On planar surfaces, perpendicular orientation can be achieved by controlling the thickness of the block copolymer (BCP) on surfaces weakly preferential to either block, while on nonpreferential surfaces, perpendicular orientation is independent of thickness within 0.8d0–1.8d0 range. In chemically homogeneous trenches, lateral alignment of domains is effectively controlled by having a chemical composition that is weakly preferential to either block, rather than perfectly nonpreferential wetting condition. By defining these boundary conditions, the nucleation of the domains can be induced primarily from the side walls rather than from the trench bottom. However, in chemically heterogeneous graphoepitaxial geometry, the BCP domains are aligned along the trench walls in both perfectly nonpreferential and weakly preferential conditions. In both the homogeneous and heterogeneous approaches, the thickness is critical for perpendicular orientation on weakly preferential surfaces. These findings affirm that graphoepitaxial assembly behavior of asymmetric BCP is governed by the interplay of surface wetting characteristics and the thickness of BCP.