Self-assembly is widely seen as the method of choice for the bottom-up manufacture of supra-colloidal aggregates. Surfactants have been used extensively to appreciate qualitatively and quantify driving forces and methodologies for controlling self-assembling processes and the resultant self-assembled aggregates. However, not much is known regarding self-assembled surfactant aggregates formed on heterogeneous surfaces. If heterogeneous surface features affect the morphology of surfactant aggregates, it is possible that new templating methodologies could be designed by engineering surfaces. Here we report equilibrium dissipative particle dynamics simulation results for surfactants adsorbed on model heterogeneous surfaces. Our simulation results reveal that, depending on the morphological and chemical properties of the solid substrate, a number of not-before-reported structures can be obtained for the self-assembled aggregates. The results presented could be useful for the manufacture of new coatings and materials, e.g., via the admicellar polymerization procedure, as well as for interpreting experimental data for surfactant adsorption on heterogeneous surfaces.