We determine the behavior of chains that are grafted in restricted geometries, such as a planar stripe of finite width and around a circular pore. Immersed in a poor solvent, the chains associate into a variety of complexes. By calculating the free energy of these complexes, we determine how their sizes scale with chain length, solvent quality, grafting density, and the dimensions of the substrate. We also construct a "phase diagram" for the possible morphologies that can occur in these systems. In the case of circular pores, we use Monte Carlo simulations to visualize the structure of the associated complexes. The results reveal how edge effects can be exploited to design polymer layers that provide protective coatings or regulate the flow of molecules through tile substrate.