  Systems evolving through aggregation and fragmentation may possess an
intriguing super-cluster state (SCS). Clusters constituting this state are
mostly large, so the SCS resembles a gelling state. The formation of the SCS is
controlled by fluctuations and in this aspect, it is similar to a critical
state. The SCS is non-extensive as the number of clusters varies sub-linearly
with the system size. In the parameter space, the SCS separates equilibrium and
jamming (extensive) states. The conventional methods such as the van Kampen
expansion fail to describe the SCS. To characterize the SCS, we propose a
scaling approach with a set of critical exponents. Our theoretical findings are
in good agreement with numerical results.
