  We obtain sharp asymptotic estimates on the number of $n \times n$
contingency tables with two linear margins $Cn$ and $BCn$. The results imply a
second order phase transition on the number of such contingency tables, with a
critical value at \ts $B_{c}:=1 + \sqrt{1+1/C}$. As a consequence, for \ts
$B>B_{c}$, we prove that the classical \emph{independence heuristic} leads to a
large undercounting.
