  A binary mixture of two-different-sizes proliferating motile disks is
studied. As growth is space-limited, we focus on the conditions such that there
is coexistence of both large and small disks, or dominance of the larger disks.
The study involves systematically varying some system parameters, such as
diffusivities, growth rates, and self-propulsion velocities. In particular, we
demonstrate that diffusing faster confers a competitive advantage, so that
larger disks can in the long time coexist or even dominate to the smaller ones.
In the case of self-propelled disks a coexistence regime is induced by the
activity where the two types of disks show the same spatial distribution: both
phase separated or both homogenously distributed in the whole system.
