  We present a new model of homogeneous aggregation that contains the essential
physical ideas of the classical predecessors, the Becker-Doring and
Lifshitz-Slyovoz models. These classical models, which give different
predictions, are asymptotic limits of the new model at small (BD) and large
(LS) cluster sizes. Since the new theory is valid for large and small clusters,
it allows for a complete description of the nucleation process; one that can
predict the creation of super-critical clusters at the Zeldovich nucleation
rate, and the diffusion limited growth of large clusters during coarsening. By
retaining the physically valid ingredients from both models, we explain the
seeming incompatibilities and arbitrary choices of the classical models.
