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We first identify the limit of the Barenblatt solutions as the solution of a fractional obstacle problem, and we observe that, contrary to the case $s=1$, the limit is not compactly supported but exhibits a typical fractional tail with power-like decay. 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We first identify the limit of the Barenblatt solutions as the solution of a fractional obstacle problem, and we observe that, contrary to the case $s=1$, the limit is not compactly supported but exhibits a typical fractional tail with power-like decay. 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