Of the three traditional techniques that have been most reliable in their application to polymers for determining molecular weight averages, only ultracentrifugal sedimentation equilibrium analyses can provide information directly about the polydispersity of a solute. Thus, when used in conjunction with size exclusion chromatography, analytical ultracentrifugation is uniquely suited to examining how polydispersity varies with the hydrodynamic volume of the species that constitute a polymeric sample. Almost impeccable fidelity has now been attained in fitting, to empirical sedimentation equilibrium data, sums of exponential terms that formally reflect the distributions of ideal macromolecular solute components in the centrifugal field. Although the component molecular weights and corresponding concentrations in each case represent principally the values of adjustable parameters that satisfy the curve fit, the ensuing z-average molecular weights have become, perhaps for the first time, quite reliable; even the weight-average molecular weights exhibit appreciable sensitivity to the degree of refinement ultimately achieved. The approach has been successfully applied to the characterization of lignin derivatives, which are complicated mixtures of macromolecular complexes and individual components; fortunately these species are not usually interconverted rapidly under the ultracentrifugal conditions employed. Not surprisingly, such fitting of exponential terms to sedimentation equilibrium data is even more straightforward for paucidisperse polystyrene fractions.