A polymerization process for producing highly branched polyesters is disclosed comprising reacting a multi-functional di- or higher epoxide group containing compound with a multi-functional di- or higher acid chloride group containing compound, wherein at least one of the epoxide or acid chloride group containing compounds is a tri- or higher epoxide or acid chloride group containing compound. The invention provides a process for producing highly branched polyesters in one reaction step. The present process comprises a ring opening reaction between a reactant or reactants having multiple epoxide groups and another reactant or reactants having multiple acid chloride groups. The invention has the capability of making highly branched structures of high molecular weight and has the advantages of not requiring multi-step reactions and purification. The invention yields highly branched polyesters having a multiplicity of very reactive epoxy or acid chloride or both on the outside surface which can be further converted to other functional groups, including polymerizable groups and initiating groups, which can undergo further chain extensions.