In this paper, fine particulate matter (PM) evolution and deposition in pulverized coal combustion are simulated by solving the population balance equation using a quadrature-based method of moment. We first verify the stability of moment closure systems for the univariate nucleation-condensation/vaporization problem and some specific coagulation/breakage problems. A series of mechanistic experiments in a 25 kW pulverized coal combustor are used for comparison and validation. The simulated particle size distributions at different combustion stages agree reasonably well with the measurements. For sub-micrometer particle evolution at the early stage of bituminous coal combustion, soot oxidation is a main driving force. While in the post-flame region when burning sodium-rich Zhundong coal, the competing processes of condensation and homogeneous nucleation of Na2SO4 vapor yield ultrafine PM0.2 with a uniform content of Na. At the burnout region (similar to 1100 K), the sodium residual in the gas is in the form of NaCl. Ash deposition experiments in this region cause mineral to transport toward the probe. We reveal that, for burning Zhundong coal, homogeneous nucleation of NaCl vapor can hardly take place in the boundary layer. The vapor condensation flux onto the probe surface takes only 4% of the flux onto pre-existing fly ash particles, whose surface stickiness may be significantly enhanced.