  We prove bilateral capacitary estimates for the maximal solution $U_F$ of
$-\Delta u+u^q=0$ in the complement of an arbitrary closed set $F\subset\mathbb
R^N$, involving the Bessel capacity $C_{2,q'}$, for $q$ in the supercritical
range $q\geq q_{c}:=N/(N-2)$. We derive a pointwise necessary and sufficient
condition, via a Wiener type criterion, in order that $U_F(x)\to\infty$ as
$x\to y$ for given $y\in\prt F$. Finally we prove a general uniqueness result
for large solutions.
