  We start investigating the extension of the Horizon Quantum Mechanics to the
case of spheroidal sources. We first study the location of trapping surfaces in
space-times resulting from an axial deformation of static isotropic systems,
and show that the Misner-Sharp mass evaluated on the corresponding undeformed
spherically symmetric space provides the correct gravitational radius to locate
the horizon. We finally propose a way to determine the deformation parameter in
the quantum theory.
