  We present a model of bi-phasic vesicle in the limit of large surface
tension. In this regime, the vesicle is completely stretched and well described
by two spherical caps with a fold which concentrates the membrane stress. The
conservation laws and geometric constraints restrict the space of possible
shapes to a pair of solutions labeled by a parameter $\tau$ given by {\it line
tension/pressure}. For a given $\tau$ value, the two solutions differ by the
length of the interface between domains. For a critical value $\tau\_c$, the
two vesicle shapes become identical and no solution exists above this critical
value. This model sheds new light on two proposed mechanisms (osmotic shocks
and molecule absorption) to explain the budding and the fission in recent
experiments.
