  The 2-dimensional Hamming graph H(2,n) consists of the $n^2$ vertices
$(i,j)$, $1\leq i,j\leq n$, two vertices being adjacent when they share a
common coordinate. We examine random subgraphs of H(2,n) in percolation with
edge probability $p$, so that the average degree $2(n-1)p=1+\epsilon$. Previous
work by van der Hofstad and Luczak had shown that in the barely supercritical
region $n^{-2/3}\ln^{1/3}n\ll \epsilon \ll 1$ the largest component has size
$\sim 2\epsilon n$. Here we show that the second largest component has size
close to $\epsilon^{-2}$, so that the dominant component has emerged. This
result also suggests that a {\it discrete duality principle} might hold,
whereby, after removing the largest connected component in the supercritical
regime, the remaining random subgraphs behave as in the subcritical regime.
