  Aggregation of animal cells in culture comprises a series of motility,
collision and adhesion processes of basic relevance for tissue engineering,
bioseparations, oncology research and \textit{in vitro} drug testing. In the
present paper, a cluster-cluster aggregation model with stochastic particle
replication and chemotactically driven motility is investigated as a model for
the growth of animal cells in culture. The focus is on the scaling laws
governing the aggregation kinetics. Our simulations reveal that in the absence
of chemotaxy the mean cluster size and the total number of clusters scale in
time as stretched exponentials dependent on the particle replication rate.
Also, the dynamical cluster size distribution functions are represented by a
scaling relation in which the scaling function involves a stretched exponential
of the time. The introduction of chemoattraction among the particles leads to
distribution functions decaying as power laws with exponents that decrease in
time. The fractal dimensions and size distributions of the simulated clusters
are qualitatively discussed in terms of those determined experimentally for
several normal and tumoral cell lines growing in culture. It is shown that
particle replication and chemotaxy account for the simplest cluster size
distributions of cellular aggregates observed in culture.
