  Neutron stars are known to host extremely powerful magnetic fields. Among
other effects, one of the consequences of harbouring such fields is the
deformation of the neutron star structure, leading, together with rotation, to
the emission of continuous gravitational waves. On the one hand, the details of
their internal magnetic fields are mostly unknown. Likewise, their internal
structure, encoded by the equation of state, is highly uncertain. Here we
present a study of axisymmetric models of isolated magnetised neutron stars,
for various realistic equations of state considered viable by observations and
nuclear physics constraints. We show that it is possible to find simple
relations between the magnetic deformation of a neutron star, its Komar mass
and its circumferential radius. Such relations are quasi-universal, meaning
that they are mostly independent on the equation of state of the neutron star
and only slightly dependent on the magnetic field configuration. Being
formulated in terms of potentially observable quantities, as we discuss, our
results could help to constrain the magnetic properties of the neutron star
interior and to better assess the detectability of continuous gravitational
waves by isolated neutron stars, without knowing their equation of state. Our
results are derived both in general relativity and in scalar-tensor theories -
one of the most promising extensions of general relativity - in this case by
considering also the scalar charge. We show that even in this case general
relations hold that account for deviations from general relativity, that could
potentially be used to set constraints on the gravitational theory.
