  We study models of spatial growth processes where initially there are sources
of growth (indicated by the colour green) and sources of a growth-stopping
(paralyzing) substance (indicated by red). The green sources expand and may
merge with others (there is no `inter-green' competition). The red substance
remains passive as long as it is isolated. However, when a green cluster comes
in touch with the red substance, it is immediately invaded by the latter, stops
growing and starts to act as red substance itself. In our main model space is
represented by a graph, of which initially each vertex is randomly green, red
or white (vacant), and the growth of the green clusters is similar to that in
first-passage percolation. The main issues we investigate are whether the model
is well-defined on an infinite graph (e.g. the $d$-dimensional cubic lattice),
and what can be said about the distribution of the size of a green cluster just
before it is paralyzed. We show that, if the initial density of red vertices is
positive, and that of white vertices is sufficiently small, the model is indeed
well-defined and the above distribution has an exponential tail. In fact, we
believe this to be true whenever the initial density of red is positive. This
research also led to a relation between invasion percolation and critical
Bernoulli percolation which seems to be of independent interest.
