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The rate equation for exchange-driven aggregation of monomers betweenclusters of size $n$ by power-law exchange rate ($\sim{n}^\alpha$), wheredetaching and attaching processes were considered separately, is reduced toFokker-Planck equation. Its exact solution was found for unbiased aggregationand agreed with asymptotic conclusions of other models. Asymptotic transitionswere found from exact solution to Weibull/normal/exponential distribution, andthen to power law distribution. Intermediate asymptotic size distributions werefound to be functions of exponent $\alpha$ and vary from normal ($\alpha=0$)through Weibull ($0<\alpha<1$) to exponential ($\alpha=1$) ones, that gives thenew system for linking these basic statistical distributions. Simulations wereperformed for the unbiased aggregation model on the basis of the initial rateequation without simplifications used for reduction to Fokker-Planck equation.The exact solution was confirmed, shape and scale parameters of Weibulldistribution (for $0<\alpha<1$) were determined by analysis of cumulativedistribution functions and mean cluster sizes, which are of great interest,because they can be measured in experiments and allow to identify details ofaggregation kinetics (like $\alpha$). In practical sense, scaling analysis of\emph{evolving series} of aggregating cluster distributions can give much morereliable estimations of their parameters than analysis of \emph{solitary}distributions. It is assumed that some apparent power and fractal laws observedexperimentally may be manifestations of such simple migration-drivenaggregation kinetics even.

Generalized Model of Migration-Driven Aggregate Growth - Asymptotic Distributions, Power Laws and Apparent Fractality