  Our ability to interpret and glean useful information from the large body of
observations of strongly magnetised neutron stars rests largely on our
theoretical understanding of magnetic field equilibria. We answer the following
question: is one free to arbitrarily prescribe magnetic equilibria such that
fluid degrees of freedom can balance the equilibrium equations? We examine this
question for various models for neutron star matter; from the simplest
single-fluid barotrope to more realistic non-barotropic multifluid models with
superfluid/superconducting components, muons and entropy. We do this for both
axi- and non-axisymmetric equilibria, and in Newtonian gravity and general
relativity. We show that, in axisymmetry, the most realistic model allows
complete freedom in choosing a magnetic field equilibrium whereas
non-axisymmetric equilibria are never completely arbitrary.
