  We performed an {\it ab initio} investigation on the properties of rutile tin
oxide (SnO$_{x}$) nanowires. We computed the wire properties determining the
equilibrium geometries, binding energies and electronic band structures for
several wire dimensions and surface facet configurations. The results allowed
to establish scaling laws for the structural properties, in terms of the
nanowire perimeters. The results also showed that the surface states control
most of the electronic properties of the nanowires. Oxygen incorporation in the
nanowire surfaces passivated the surface-related electronic states, and the
resulting quantum properties and scaling laws were fully consistent with
electrons confined inside the nanowire. Additionally, oxygen incorporation in
the wire surfaces generated an unbalanced concentration of spin up and down
electrons, leading to magnetic states for the nanowires.
