With increasing hydrophilic to hydrophobic (f) block ratio the preferred morphology for self-assembly of block copolymers in solution changes from membranes (bilayer vesicles) to worm-like micelles to spherical micelles. Drug delivery using block copolymer carriers is thought to have significant advantages over more established delivery methods such as liposome encapsulation, but polydispersity of the diblock chains can easily be 10 times that of lipid systems and raise questions about the effects on the overall phase behavior. Curvatures of polymer vesicle membranes could be influenced and shifts toward higher f by degradation – with unavoidable increases in polydispersity – are providing key mechanisms for release (eg. Ahmed and Discher, J. Control. Release 2004). Similar f-based segregation has also been suggested for worm-like to spherical micelle transitions, with diffusion of the high-f chains to the ends of the worms. Here we measure the effects of polydispersity on the stability of block copolymer assemblies by using coarse-grained molecular dynamics simulations. By measuring the free energy of aggregation of high f chains in a membrane as a function of polydispersity we can find the degree of polydispersity associated with pore formation in a membrane. To understand the transition of worms to spherical micelles, the dynamics of the worm terminus is studied under the influence of polydispersity. In this manner, we measure the polydispersity required for key transitions being exploited in drug delivery from block copolymer carriers.