  We study the dynamics of diffusion-limited irreversible aggregation of
monomers, where bonds are mediated by linkers. We combine kinetic Monte Carlo
simulations of a lattice model with a mean-field theory to study the dynamics
when the diffusion of aggregates is negligible and only monomers diffuse. We
find two values of the number of linkers per monomer which maximize the size of
the largest aggregate. We explain the existence of the two maxima based on the
distribution of linkers per monomer. This observation is well described by a
simple mean-field model. We also show that a relevant parameter is the ratio of
the diffusion coefficients of monomers and linkers. In particular, when this
ratio is close to ten, the two maxima merge at a single maximum.
