We consider some generalizations of the germ-grain growing model studied by Daley, Mallows and Shepp (2000). In this model, a realization of a Poisson process on a line with points X
i is fixed. At time zero, simultaneously at each X
i, a circle (grain) starts growing at the same speed. It grows until it touches another grain, and then it stops. The question is whether the
... [Show full abstract] point zero is eventually covered by some circle. In our note we expand this model in the following three directions. We study: a one-sided growth model with a fixed number of circles; a grain-growth model on a regular tree; and a grain-growth model on a line with non-Poisson distributed centres of the circles.
