  We consider the model of Deijfen et al. for competing growth of two infection
types in R^d, based on the Richardson model on Z^d. Stochastic ball-shaped
infection outbursts transmit the infection type of the center to all points of
the ball that are not yet infected. Relevant parameters of the model are the
initial infection configuration, the (type-dependent) growth rates and the
radius distribution of the infection outbursts. The main question is that of
coexistence: Which values of the parameters allow the unbounded growth of both
types with positive probability? Deijfen et al. conjectured that the initial
configuration basically is irrelevant for this question, and gave a proof for
this under strong assumptions on the radius distribution, which e.g. do not
include the case of a deterministic radius. Here we give a proof that doesn't
rely on these assumptions. One of the tools to be used is a slight
generalization of the model with immune regions and delayed initial infection
configurations.
