A rigorous model is developed to predict the configurations of the branched polymers formed by the copolymerization of linear monomers in the presence of multifunctional branching units. Conventional studies on the configuration of branched polymers generally consider the statistical properties of the growth of only one element or polymerization from one component (e.g., dendrimers, hyperbranched, and hypergrafted polymers from ABm or ABC-type monomers). This study considers combinations of several types of linear and branched elements and the simultaneous aggregation of branched element branched element and monomer-monomer elements. The proposed method is based on a new conceptual model that splits a multifunctional unit into a set of seeds with each functional group, assembling the branched elements after the independent propagation of each seed. Accordingly, the propagation steps of each element are described as dynamic balance equations in terms of the moments of the number chain length distribution. Analysis of the simulation of a batch sulfonated poly(aryl ether ketone) copolymerization process with trifunctional units is performed with the proposed model. The simulation results show that the proposed model reflects the characteristics of real copolymerization processes. (C) 2017 Elsevier Ltd. All rights reserved.