A review on the synthesis of unsaturated polyester (UP) prepolymers showed that Ordelt saturation (reaction of hydroxyl groups with double bonds) is the major effect that may cause formation of chain branches and then result in an uncertainty of chain end number or functionality. A model has been derived in this work to estimate the number of chain branches and the number of chain ends of UP prepolymers from several fundamental molecular parameters, including hydroxyl and carboxyl indexes, Ordelt saturation extent, short- and long-chain branch distribution, molecular polydispersity, and starting reactant composition and also reasonable assumptions concerning the chain-branch lengths. Simulation results were compared with experimental ones. The influences of the mentioned molecular parameters on the chain branches and on the overall molecular chain ends are discussed in this work.