We study a model in which two entities (e.g., plant species, political
ideas,...) compete for space on a plane, starting from randomly distr
ibuted seeds and growing deterministically at possibly different rates
. An entity which forms an infinite cluster is considered to dominate
over the other (which then cannot percolate). We analyze the occurrenc
e of such a form of domination in situations in which one entity start
s from a much larger density of seeds than the other one, but the latt
er one grows at a much faster rate than the former one. The model stud
ied here generalizes the problem of Voronoi percolation.