An off-lattice model of a vesicle assembly in two dimensions is studie
d by use of computer simulation techniques. The vesicles are represent
ed as closed, self-avoiding tethered chains with bending rigidity. We
present studies for a system of fluctuating vesicle configurations, wh
ere the total number of monomers is fixed, but the vesicle size distri
bution may vary, i.e. the vesicles can fuse or break up. The phase dia
gram obtained in the case of zero osmotic pressure contains a vesicle
phase with broken in-out symmetry and a symmetric ''bicontinuous'' pha
se. The phases are separated by a line of Ising-type second-order phas
e transitions, and the functional form of the phase boundary is derive
d from simple scaling arguments.