  We study the evolution of aggregates triggered by collisions with monomers
that either lead to the attachment of monomers or the break-up of aggregates
into constituting monomers. Depending on parameters quantifying addition and
break-up rates, the system falls into a jammed or a steady state. Supercluster
states (SCSs) are very peculiar non-extensive jammed states that also arise in
some models. Fluctuations underlie the formation of the SCSs. Conventional
tools, such as the van Kampen expansion, apply to small fluctuations. We go
beyond the van Kampen expansion and determine a set of critical exponents
quantifying SCSs. We observe continuous and discontinuous phase transitions
between the states. Our theoretical predictions are in good agreement with
numerical results.
