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We consider random states on $\\C^d \\otimes \\C^d$ obtained by partial tracing a Haar-distributed random pure state on $\\C^d \\otimes \\C^d \\otimes \\C^s$ over an ancilla space $\\C^s$. We show that, for large $d$, the realignment criterion typically detects entanglement if and only if $s \\leq (8/3\\pi)^2 d^2$. 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