  The conformation and scaling properties of self-avoiding fluid vesicles with
zero extrinsic bending rigidity subject to an internal pressure increment
$\Delta p>0$ are studied using Monte Carlo methods and scaling arguments. With
increasing pressure, there is a first-order transition from a collapsed
branched polymer phase to an extended inflated phase. The scaling behavior of
the radius of gyration, the asphericities, and several other quantities
characterizing the average shape of a vesicle are studied in detail. In the
inflated phase, continuously variable fractal shapes are found to be controlled
by the scaling variable $x=\Delta p N^{3\nu/2}$ (or equivalently, $y = {<V>}/
N^{3\nu/2}$), where $N$ is the number of monomers in the vesicle and $V$ the
enclosed volume. The scaling behavior in the inflated phase is described by a
new exponent $\nu=0.787\pm 0.02$.
