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At each step those vertices which have more active neighbours than inactive neighbours become active as well.\n  We study the size $A^*$ of the final active set. The parameters of the model are, besides $n$ (tending to $\\infty$), the size $A(0)=A_0(n)$ of the initially active set and the probability $p=p(n)$ of the edges in the graph. We prove that the process cannot percolate for $A(0) = o(n)$. 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