The collection efficiency of particles in the nanosize range (5-100 nm) in a two stage parallel plate electrostatic precipitator is studied by numerical simulation based on a fundamental model of the process. Specifically, the particle charging process is based on Fuchs' theory. For the collecting stage, the model employs an Eulerian approach for the solid-gas flow and explicitly accounts for Brownian and eddy diffusion, turbulent flow, and electrostatic migration. Calculation results indicate that particles in the nanosize range are not uniformly charged. Ultrafine particles with diameter less than 20 nm seldom acquire more than one unit of elementary charge. Larger particles (20-100 nm) may carry several units of charge, depending on the product of ion concentration and charging time. The simulation results also indicate that there is a local maximum in the collection efficiency in the nanosize range, a finding which is consistent with experimental observations reported in the literature. The simulation also points out that the most efficient way to increase the collection efficiency of particles in the ultrafine size range is to enhance the charging process. For particles with larger size, both the parameters in the charging stage (the product of ion concentration and charging time) and those in the collecting stage (electrostatic intensity and length and width of the collecting cell) have an important effect on the overall collection efficiency.