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This paper analytically investigates the steady-state properties of a practical power distribution system with unbalanced loads, single-, two-, and three-phase lines and transformers of different connection types. It is shown that the three-phase power flow solution with feasible voltage magnitude for radial three-phase distribution networks with nonlinear load modeling always exists and is unique. Also, motivated by the practical use of three-phase power flow analysis as a basic tool for distribution system application functions, monotonic properties of the voltage magnitude at each node with respect to load changes are established. Implications and applications of these analytical results to distribution system analysis and design are discussed.