Nonsolvent-induced precipitation processes may generate an asymmetric morphology from an initially single-phase homogeneous polymer solution. In these processes, mass transfer induces phase separation and subsequent vitrification eliminates further reorganization of a polymer-rich phase. Kinetics is responsible for trapping specific morphologies and can be influenced by local composition, temperature, applied stress, and preexisting nuclei. Focusing only on the influence of composition changes, the growth of a preformed hypothetical nucleus in a metastable region is considered during rapid phase separation induced by an advancing front that is rich in nonsolvent for the dissolved polymer. Expansion of the preformed nucleus can be promoted by osmotically-generated forces arising from a net volumetric accumulation of fluid in the nucleus. Growth of the nucleus is opposed by the vitrification of the polymer-rich matrix surrounding the nucleus. The process described produces structures, typically referred to as macrovoids, which are undesirable features and tend to reduce the mechanical strength of the membrane. Thus, the balance between the local volumetric rate of solvent-nonsolvent exchange compared to the vitrification rate are key factors in the growth or suppression of macrovoids. This process may be controlled by altering the initial dope composition, the nature of the various additives, and the rates of mass transfer (specifically across the nucleus wall), by imposing temperature gradients or by altering the external quench bath composition.