  We characterize the well known self-similar Blasius profiles, $[\bar{u},
\bar{v}]$, as downstream attractors to solutions $[u,v]$ to the 2D, stationary
Prandtl system. It was established in \cite{Serrin} that $\| u -
\bar{u}\|_{L^\infty_y} \rightarrow 0$ as $x \rightarrow \infty$. Our result
furthers \cite{Serrin} in the case of localized data near Blasius by
establishing convergence in stronger norms and by characterizing the decay
rates. Central to our analysis is a "division estimate", in turn based on the
introduction of a new quantity, $\Omega$, which is globally nonnegative
precisely for Blasius solutions. Coupled with an energy cascade and a new
weighted Nash-type inequality, these ingredients yield convergence of $u -
\bar{u}$ and $v - \bar{v}$ at the essentially the sharpest expected rates in
$W^{k,p}$ norms.
