Power-law size distribution of supercritical random trees

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The probability distribution P(k) of the sizes k of critical trees (branching ratio m=1) is well known to show a power-law behavior k(-3/2). Such behavior corresponds to the mean-field approximation for many critical and self-organized critical phenomena. Here we show numerically and analytically that also supercritical trees (branching ration m>1) are "critical" in that their size distribution obeys a power-law k(-2). We mention some possible applications of these results.