Clustering of clusters processes above their upper critical dimensionalities

In contrast with the diffusion limited particle-cluster aggregation (P-Cl), the cluster-cluster aggregation model (Cl-Cl) has a finite upper critical dimensionality above which the fractal dimension of the clusters is trivial. This exponent is derived analytically for a whole set of models, including P-Cl and Cl-Cl. The results clarify the physical differences between these two models.