  We investigate irreversible aggregation processes driven by a source of small
mass clusters. In the spatially homogeneous situation, a well-mixed system is
consists of clusters of various masses whose concentrations evolve according to
an infinite system of nonlinear ordinary differential equations. We focus on
the cluster mass distribution in the long time limit. An input-driven
aggregation with rates proportional to the product of merging partners
undergoes a percolation transition. We examine this process analytically and
numerically. There are two theoretical schemes and two natural ways of
numerical integration on the level of a truncated system with a finite number
of equations. After the percolation transition, the behavior depends on the
adopted approach: The giant component quickly engulfs the entire system (Flory
approach), or a non-trivial stationary mass distribution emerges (Stockmayer
approach). We also outline generalization to ternary aggregation.
