  We investigate analytically and numerically a system of clusters evolving via
collisions with clusters of minimal mass (monomers). Each collision either
leads to the addition of the monomer to the cluster or the chipping of a
monomer from the cluster, and emerging behaviors depend on which of the two
processes is more probable. If addition prevails, monomers disappear in a time
that scales as $\ln N$ with the total mass $N\gg 1$, and the system reaches a
jammed state. When chipping prevails, the system remains in a quasi-stationary
state for a time that scales exponentially with $N$, but eventually, a giant
fluctuation leads to the disappearance of monomers. In the marginal case,
monomers disappear in a time that scales linearly with $N$, and the final
supercluster state is a peculiar jammed state, viz., it is not extensive.
