We study living polymerization initiated from concave surfaces. We clarify that, depending on different criteria for ceasing the reaction, different relationships between grafted chain polydispersity index and the grafting surface curvature can be categorized. The average molecular weight of the grafted chains monotonically decreases as the grafting surface curvature increases. These results shed light on better control and design of functional porous materials for use in bioimplanting or chemical sensors.