  We analyze a general class of reversible aggregate-reorganization processes.
These processes are shown to exhibit globally attracting equilibrium
distributions, which are \textit{universal}, i.e. identical for large classes
of models. Furthermore, the analysis implies that for studies of equilibrium
properties of \textit{any} such process, computationally expensive
reorganization dynamics such as random walks can be replaced by more efficient,
yet simpler methods. As a particular application, our results explain the
recent observation of the formation of similar fractal aggregates from
different initial structures by diffusive reorganization [Filoche and Sapoval,
Phys. Rev. Lett. 85, 5118 (2000)].
