The formation of adsorbed surfactant layers consisting of a mesh or network of branched cylindrical aggregates on muscovite mica by several surfactant systems is described. The curvature of the adsorbed aggregates is varied by a variety of mechanisms that all generate morphologies between adsorbed cylinders and bilayers, and the resulting lateral structure is imaged by "soft contact" atomic force microscopy. We compare the direct images and Fourier transforms of the adsorbed layer structures, and relate them to those formed in bulk solution.