Mimicking the complex morphological transformations of living cells is an area of ongoing interest to membrane scientists. To this end, liposomes and surfactant vesicles are often regarded as adequate membrane models. Here, we report the morphological transformations reminiscent of endocytosis and vesicular transport for a very basic model system. It is demonstrated that structural conversions of vesicles composed of dioctadecyldimethylammonium salts are triggered by the presence of the cationic initiator V50. On the basis of experimental data (cryo transmission electron microscopy, dynamic light scattering, and turbidity measurements) and theoretical considerations, we propose and discuss a phenomenological model that accounts for these observations. It is shown that even simple triggers can give rise to interesting and complex morphological transformations. Finally, polymerizations of styrene in these model vesicle systems are performed, and it appears that the vesicle transformations have a pronounced effect on the final vesicle-polymer morphology.