  We study the set of points $\mathcal{D}_{n,m}$ around which two independent
Brownian motions wind at least $n$ (resp. $m$) times. We prove that its area is
asymptotically equivalent, in $L^p$ and almost surely, to
$\frac{\ell(\mathbb{R}^2)}{4\pi^2 n m}$, where $\ell$ is the intersection
measure of the two trajectories. We also prove that the properly scaled
Lebesgue measure carried by $\mathcal{D}_{n,m}$ converges almost surely weakly
toward $\ell$.
