The invention relates to a method for the production of a branched polycarbonate composition, having increased melt strength, by late addition of branch-inducing catalysts to the polycarbonate oligomer in a melt polycondensation process. Surprisingly, it has been found that by adding branch-inducing catalysts, such as alkali metal compounds and/ or alkaline earth metal compounds, to the melt polycarbonate oligomer at a later stage of the melt polycondensation process, preferably after the oligomer has reached an average molecular weight of between about 3,000 and 30,000 g/mole, a unique branched polycarbonate composition is formed that has improved properties. It is believed that the addition of the branch-inducing catalysts at the later stages of the process produces a branched polycarbonate composition having longer chains between the branching points, and thus a new composition is produced. The invention also relates to various applications of the branched polycarbonate composition.