The self-assembly of cationic and nonionic surfactants on hydrophilic surfaces is considered. By computing the equilibrium free-energy for the formation of a given structure, the critical surfactant concentration for the formation of surface aggregates (CAC) and the surface morphology are predicted. The CAC is always predicted to be lower than the bulk phase critical micelle concentration (CMC). In addition to the full spheres and cylinders that have been proposed in the literature, a series of composite structures are proposed which are composed of monolayers oriented with head groups in contact with the surface and covered with either hemispheres, hemicylinders, finite disks, or another monolayer (making the full structure a bilayer). It is shown that for several illustrative cases, composite hemicylinders will form at the CAC. Since the surfactant concentration required for the formation of full spherical and full cylindrical surface aggregates is largely comparable to the bulk CMC, it is likely that the surface structures observed in atomic force microscopy (AFM) experiments conducted near the bulk CMC are not full spheres or cylinders, but the corresponding composite structures made up of hemispheres or hemicylinders.