A review is presented of the pioneering 1950 model (V. K. LaMer, R. H. Dinegar, Theory, Production and Mechanism of Formation of Monodispersed Hydrosols, J. Am. Chem. Soc., 1950, 72, 4847-4854) of how monodisperse particles might possibly be formed. The review begins with a look at the basis of the 1950 model in fluctuation and classical nucleation theories. Presented next are the competing phase-change models and then also chemical mechanisms for particle formation available since the 1950 paper, including a little-cited nucleation mechanism that LaMer insightfully wrote in 1952. This review then takes a critical look at the 164 (similar to 8%) of the 192 total (similar to 10%) out of the 1953 papers (as of March 2019) that cite the 1950 model while also providing at least some discussion, analysis, or additional data bearing on the 1950 model postulating "effectively infinite nucleation" and "diffusion-controlled growth". (The other 28 papers out of the 192 total papers describe S-n sol formation were covered in an earlier, Part I review that is cited.) Those 164 papers are broken down into five tables provided in the Supporting Information and are then covered in separate sections in the main text: first 13 papers on silver halide nanoparticles (Table S1) where the single best evidence in support of the 1950 model has been thought to exist; 26 papers on semiconductor nanoparticles (Table S2); then 69 papers on transition-metal nanoparticle formation (Table S3); 39 papers on oxide-based nanoparticles (Table S4); and 17 papers presenting alternative models or mechanisms in comparison to the 1950 model (Table S5). The review focuses on answering the critical question of: do the concepts of "burst/instantaneous nucleation" and "diffusion-controlled growth" have sound, compelling experimental support in the 70 years since the model first appeared and in the 164 papers examined more closely that do more than just cite the 1950 model? A Conclusions section listing sixteen bullet points is provided, as is a final section entitled "A Look Towards the Future" that discusses evolving areas and suggested emphasis points for facilitating future research in particle formation kinetics, mechanism and associated particle syntheses.