The surface aggregates structure of dimethyldodecylamine-N-oxide (C12DAO) in three silica dispersions of different particle sizes (16 - 42 nm) was studied by small-angle neutron scattering (SANS) in a H2O/D2O solvent mixture matching the silica. At the experimental conditions (pH 9) the surfactant exists in its nonionic form and the structure of the adsorbed layer is not affected by added electrolyte. It is found that C12DAO forms spherical surface micelles of 2 nm diameter on the 16 nm silica particles, but oblate ellipsoidal surface micelles are formed on the 27 and 42 nm particles. The dimensions of these oblate surface aggregates (minor and major semi-axes Rn and Rlat) are similar to those of C12DAO micelles in the aqueous solutions. It is concluded that the morphological transition from spherical to ellipsoidal surface aggregates is induced by the surface curvature of the silica particles. A comparison of the shape and dimensions of the surface aggregates formed by C12DAO and C12E5 on the 16 nm silica particles demonstrates that the nature of the surfactant head group does not determine the morphology of the surface aggregates, but has a strong influence on the number of surface aggregates per particle, due to the different interactions of the head groups with the silica surface.