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We introduce a stochastic model in which adjacent planar regions $A, B$ mergestochastically at some rate $\lambda(A,B)$, and observe analogies with thewell-studied topics of mean-field coagulation and of bond percolation. Doinfinite regions appear in finite time? We give a simple condition on $\lambda$for this {\em hegemony} property to hold, and another simple condition for itto not hold, but there is a large gap between these conditions, which includesthe case $\lambda(A,B) \equiv 1$. For this case, a non-rigorous analyticargument and simulations suggest hegemony.

Empires and Percolation: Stochastic Merging of Adjacent Regions