  The Marcus-Lushnikov process is a finite stochastic particle system in which
each particle is entirely characterized by its mass. Each pair of particles
with masses $x$ and $y$ merges into a single particle at a given rate $K(x,y)$.
We consider a {\it strongly gelling} kernel behaving as $K(x,y)=x^\alpha y + x
y^\alpha$ for some $\alpha\in (0,1]$. In such a case, it is well-known that
{\it gelation} occurs, that is, giant particles emerge. Then two possible
models for hydrodynamic limits of the Marcus-Lushnikov process arise: the
Smoluchowski equation, in which the giant particles are inert, and the Flory
equation, in which the giant particles interact with finite ones. We show that,
when using a suitable cut-off coagulation kernel in the Marcus-Lushnikov
process and letting the number of particles increase to infinity, the possible
limits solve either the Smoluchowski equation or the Flory equation. We also
study the asymptotic behaviour of the largest particle in the Marcus-Lushnikov
process without cut-off and show that there is only one giant particle. This
single giant particle represents, asymptotically, the lost mass of the solution
to the Flory equation.
