Amphiphilic block copolymers of suitable proportions can self-assemble into surprisingly long and stable worm-like micelles, but the intrinsic polydispersity of polymers as well as polymer blending efforts and the increasing use of degradable chains all raise basic questions of curvature–composition coupling and morphological stability of these high curvature assemblies. Molecular simulations here of polyethylene glycol (PEG) based systems show that a systematic increase in the hydrated PEG fraction, in both monodisperse and binary blends, induces budding and breakup into spherical and novel ‘dumbbell’ micelles—as seen in electron microscopy images of degradable worm-like micelles. Core dimension, d, in our large-scale, long-time dissipative particle dynamics (DPD) simulations is shown to scale with chain-length, N, as predicted theoretically by the strong segregation limit (d ≈ N2/3), but morphological transitions of binary mixtures are only crudely predicted by simple mixture rules. Here we show that for weakly demixing diblock copolymers, the coupling between local interfacial concentration and mean curvature can be described with a simple linear relationship. The computational methods developed here for PEG-based assemblies should be useful for many high curvature nanosystems.