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Let $\\Gamma ^1$ and $\\Gamma ^2$ be two disjoint open subsets of $\\Gamma$, representing the parts of $\\Gamma$ through which some water can enter and escape from $\\Omega$. A law of large numbers for the maximal flow from $\\Gamma ^1$ to $\\Gamma ^2$ in $\\Omega$ is already known. In this paper we investigate the asymptotic behavior of a maximal stream and a minimal cutset. 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