  Magnetic fields play a critical role in the phenomenology of neutron stars.
There is virtually no observable aspect which is not governed by them. Despite
this, only recently efforts have been done to model magnetic fields in the
correct general relativistic regime, characteristic of these compact objects.
In this work we present, for the first time a comprehensive and detailed
parameter study, in general relativity, of the role that the current
distribution, and the related magnetic field structure, have in determining the
precise structure of neutron stars. In particular, we show how the presence of
localized currents can modify the field strength at the stellar surface, and we
look for general trends, both in terms of energetic properties, and magnetic
field configurations. Here we verify that, among other things, for a large
class of different current distributions the resulting magnetic configurations
are always dominated by the poloidal component of the current.
