  We study the asymptotic zero distribution of the rescaled Laguerre
polynomials, $\displaystyle L_n^{(\alpha_n)}(nz)$, with the parameter
$\alpha_n$ varying in such a way that $\displaystyle \lim_{n\rightarrow
\infty}\alpha_n/n=-1$. The connection with the so-called Szeg\"{o} curve will
be showed.
