Using Monte Carlo computer simulations, we examine the aggregation of a dilute solution of amphiphilic comb copolymers. We first consider combs that are composed of solvophobic teeth and a solvophilic backbone and determine how the strength of the interaction between the solvophobic teeth affects the self-assembly of these chains. Subsequently, we vary the number and length of the teeth, and establish how these structural variations affect the morphology of the aggregates in the solution. We finally compare the association behavior of these copolymers to combs that contain solvophobic backbones and solvophilic teeth and to linear amphiphilic chains. The results provide guidelines for synthesizing copolymers that act as effective viscosity modifiers and form amphiphilic networks for biomedical applications.