  Generalizing the well-known lilypond model we introduce a growth-maximal
hard-core model based on a space-time point process of convex particles. Using
a purely deterministic algorithm we prove under fairly general assumptions that
the model exists and is uniquely determined by the point process. Under an
additional stationarity assumption we show that the model does not percolate.
Our model generalizes the lilypond model considerably even if all grains are
born at the same time. In that case and under a Poisson assumption we prove a
central limit theorem in a large volume scenario.

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