It is shown that there is no quasi-sphere packing of the lattice grid Z^{d+1}
or a co-compact hyperbolic lattice of H^{d+1} or the 3-regular tree \times Z,
in R^d, for all d. A similar result is proved for some other graphs too. Rather
then using a direct geometrical approach, the main tools we are using are from
non-linear potential theory.

This is a short (and somewhat informal) contribution to the proceedings of
the XVIth International Congress on Mathematical Physics, Prague, 2009, written
up by the second author. We describe how the recent proof of the existence and
conformal covariance of the scaling limits of dynamical and near-critical
planar percolation implies the existence and several topological properties of
the scaling limit of the Minimal Spanning Tree, and that it is invariant under
scalings, rotations and translations.