Nanoparticles of polymethylmethacrylate (PMMA) have been produced through the solvent shifting process (also called the "Ouzo process") in which water (nonsolvent) was added to a solution of PMMA in acetone or tetrahydrofuran (solvent). At low concentrations of PMMA in the initial solution, and for large additions of water, the process yielded PMMA nanoparticles with a narrow distribution of particle sizes. The mean particle diameter varied as a power law of the initial PMMA concentration in the solvent, in agreement with the predictions from the Smoluchowski equation for an aggregation process that has definite "start" and "stop" times. At higher PMMA concentrations, the mixing process yielded microparticles coexisting with PMMA nanoparticles. The boundary that separates the Ouzo region of compositions (PMMA nanoparticles only), from the "non-Ouzo" region (nano- and microparticles) has been determined. This boundary does not appear to have any relation to the spinodal decomposition line of the ternary solutions: the transition from Ouzo to non-Ouzo behavior must have another unknown origin.