Using dissipative particle dynamics simulations the relationship between molecular architecture and phase behaviour in model hairy-rod polymers is studied. In agreement with experimental and theoretical studies the phase behaviour is controlled by changes to the molecular structure, particularly the sidechain length and density, and the molecular interactions. For dense sidechains a lamellar structure is found, which becomes an inverted cylindrical phase when the sidechain density is lowered. The ordered phases become more stable on increasing sidechain length and on increasing the repulsion strength between the backbone and sidechains. In the absence of torsional potentials the structures are double-walled, i.e. layers are two polymer backbones thick, while single-walled structures are observed for polymers with torsional potentials.