We introduce a theoretical model that predicts adsorbed configurations of asymmetric surfactant molecules on polar surfaces. This model extends the ideas developed in our previous work for predicting adsorbed configurations of linear surfactant molecules on polar surfaces. The surfactant molecules have a large polar headgroup and a linear alkyl tail. These asymmetric molecules form cylindrical/spherical morphologies in the adsorbed state. Our model predicts that the molecules adsorb either with their molecular axis parallel to the surface (lying-down configuration) or perpendicular to the surface (standing-up configuration). The standing-up and lying-down configurations result in significantly different adsorbed morphologies. In the standing-up configuration, the adsorbed morphology is like that of full cylinders, while, in the lying-down configuration, the adsorbed morphology resembles partial spheres. The standing-up configuration is obtained when the strength of interaction of the polar headgroup with the surface dominates over the interactions of the alkyl tail with the surface. When interactions of the alkyl tail are dominant, the molecules attain the lying-down configuration. Predictions from the theoretical model quantitatively match the results obtained from Langevin dynamics simulations. The theoretical model also explains the different kinetic pathways that have been reported in the experimental studies on the organization of adsorbed surfactants on polar surfaces.