This paper is the second of a series devoted to the study of the dynamics of the spectrum of large random matrices. We study general extensions of the partial differential equation arising to characterize the limit spectral measure of the Dyson Brownian motion. We show that several results of part I extend to cases in which there is no spectral dominance property. We also provide several modeling extensions of such models. Finally we establish new regularizing results for the case of the Dyson Brownian motion.