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Analyses of unipolar charge transport phenomena in series, two-region composite dielectric systems are presented for planar, coaxial cylindrical, and concentric spherical electrode geometries. Space charge limited condition is applied at the charge emitting electrode for steady state and transient. Method of characteristics is used to convert the governing partial differential equations into a set of ordinary differential equations that allow analytical solutions as functions of time and space for volume and interfacial surface charge densities, charge trajectories, electric field intensity, and voltage drop across the electrodes. Solutions given in this paper can be used in design of high-voltage capacitors, pulsed-power transmission lines, and other apparatus. These solutions have also been used as a way of gaining confidence in the correctness and accuracy of our charge transport and prebreakdown models in two-phase insulation systems.