We propose a classical density functional theory model to study the self-assembly of polymeric surfactants on curved surfaces. We use this model to investigate the thermodynamics of phase separation of a binary mixture of size asymmetric miscible surfactants on cylindrical and spherical surfaces, and observe that phase separation driven by size alone is thermodynamically unfavorable on both cylindrical and spherical surfaces. We use the theory, supplemented by dissipative particle dynamics (DPD) simulations, to predict pattern formation on a non-uniform surface with regions of positive and negative curvature. Our results suggest potential ways to couple surface topography and polymeric surfactants to design surfaces coated with non-uniform patterns.