  The growth of multicomponent structures in simulations and experiments often
results in kinetically trapped, nonequilibrium objects. In such cases we have
no general theoretical framework for predicting the outcome of the growth
process. Here we use computer simulations to study the growth of two-component
structures within a simple lattice model. We show that kinetic trapping happens
for many choices of growth rate and inter-component interaction energies, and
that qualitatively distinct kinds of kinetic trapping are found in different
regions of parameter space. In a region in which the low-energy structure is an
`antiferromagnet' or `checkerboard', we show that the grown nonequilibrium
structure displays a component-type stoichiometry that is different to the
equilibrium one but is insensitive to growth rate and solution conditions. This
robust nonequilibrium stoichiometry can be predicted via a mapping to the
jammed random tiling of dimers studied by Flory, a finding that suggests a way
of making defined nonequilibrium structures in experiment.
