  The $N\to\infty$ limit of the edges of finite planar electron densities is
discussed for higher Landau levels. For full filling, the particle number is
correlated with the magnetic flux, and hence with the boundary location, making
the $N\to\infty$ limit more subtle at the edges than in the bulk. In the
$n^{\rm th}$ Landau level, the density exhibits $n$ distinct steps at the edge,
in both circular and rectangular samples. The boundary characteristics for
individual Landau levels, and for successively filled Landau levels, are
computed in an asymptotic expansion.
