In synthesizing polymers in vivo and in vitro, molecular homogenous (“monodisperse”) polymers (i.e., those in which every macromolecule has the same molar mass or “molecular weight”) occur only under quite specific conditions. The overwhelming majority of polymer syntheses proceed more or less randomly, and the resulting macromolecular substances have more or less broad molar mass distributions. The kind of molar mass distribution obtained depends on the nature of the polymerization, which may be either thermodynamically or kinetically controlled. Each kind of distribution is characterized by a definite relationship between the mole fraction x and the degree of polymerization X. Consequently, it is possible in many cases to deduce the kind of polymerization involved from the type of distribution function obtained.