We report on a combined scanning tunneling microscopy (STM), X-ray photoelectron spectroscopy (XPS), and density functional theory (DFT) study on the surface-assisted assembly of the hexaiodo-substituted macrocycle cyclohexa-m-phenylene (CHP) toward covalently bonded polyphenylene networks on Cu(111), Au(111), and Ag(111) surfaces. STM and XPS indicate room temperature dehalogenation of CHP on either surface, leading to surface-stabilized CHP radicals (CHPRs) and coadsorbed iodine. Subsequent covalent intermolecular bond formation between CHPRs is thermally activated and is found to proceed at different temperatures on the three coinage metals. The resulting polyphenylene networks differ significantly in morphology on the three substrates: On Cu, the networks are dominated by "open" branched structures, on the Au surface a mixture of branched and small domains of compact network clusters are observed, and highly ordered and dense polyphenylene networks form on the Ag surface. Ab initio DFT calculations allow one to elucidate the diffusion and coupling mechanisms of CHPRs on the Cu(111) and Ag(111) surfaces. On Cu, the energy barrier for diffusion is significantly higher than the one for covalent intermolecular bond formation, whereas on Ag the reverse relation holds. By using a Monte Carlo simulation, we show that different balances between diffusion and intermolecular coupling determine the observed branched and compact polyphenylene networks on the Cu and Ag surface, respectively, demonstrating that the choice of the substrate plays a crucial role in the formation of two-dimensional polymers.