We introduce a simple dynamical model which can explain the development of hat-shaped surface attached liposomes by taking membrane self-adhesion into account. The model reveals that hat formation is a general phenomenon, although it is difficult to observe experimentally. We show under what conditions hat-shaped vesicles can become observable. One such scenario, in consistency with AFM measurements, is that the dynamics is slowed down by the low rate of the outflow of the internal fluid of the vesicle through the narrow space between the two bilayers of the brim.