  Soft Gamma-Ray Repeaters and Anomalous X-Ray Pulsars are extreme
manifestations of the most magnetized neutron stars: magnetars. The
phenomenology of their emission and spectral properties strongly support the
idea that the magnetospheres of these astrophysical objects are tightly twisted
in the vicinity of the star. Previous studies on equilibrium configurations
have so far focused on either the internal or the external magnetic field
configuration, without considering a real coupling between the two fields. Here
we investigate numerical equilibrium models of magnetized neutron stars endowed
with a confined twisted magnetosphere, solving the general relativistic
Grad-Shafranov equation both in the interior and in the exterior of the compact
object. A comprehensive study of the parameters space is provided to
investigate the effects of different current distributions on the overall
magnetic field structure.
