We have studied the phase behavior of zwitterionic phospholipid dioleoylphosphatidylcholine (DOPC) vesicles (membranes) and interpreted our results using scaling arguments in combination with molecular realistic self-consistent field (SCF) calculations. DOPC membranes acquire a partial negative charge per lipid molecule at intermediate NaBr concentrations. As a result of this, dilute DOPC solutions form stable unilamellar vesicles. Both at low and high salt concentrations phase separation into a lamellar and a vesicular phase is observed. The vesicle radius decreases as a power law with decreasing lipid concentration. This power-law concentration dependence indicates that the vesicle phase is entropically stabilized; the size of the DOPC vesicles result from a competition between the bending energy and translation and undulation entropy. This scaling behavior breaks down for very small vesicles. This appears to be consistent with SCF predictions that point to the fact that in this regime the mean bending modulus k(c) increases with curvature. The SCF theory predicts that, at low ionic strength, the membrane stability improves when there is more charge on the lipids. Upon a decrease of the ionic strength, lipids with a full negative charge form vesicles that grow exponentially in size because the mean bending modulus increases with decreasing ionic strength. At the same time the Gaussian bending modulus becomes increasingly negative such that the overall bending energy tends to zero. This indicates that small micelles become the dominant species. The SCF theory thus predicts a catastrophic break down of giant vesicles in favor of small micelles at sufficiently low ionic strength and high charge density on the lipids.