  We study magnetic field effects on the Equations of State (EoS) and the
structure of Bose-Einstein Condensate (BEC) stars, i.e. a compact object
composed by a gas of interacting spin one bosons formed up by the pairing of
two neutrons. To include the magnetic field in the thermodynamic description,
we suppose that particle-magnetic field and particle-particle interactions are
independent. We consider two configurations for the magnetic field: one where
it constant and externally fixed, and another where it is produced by the
bosons by self-magnetization. Since the magnetic field produces the splitting
of pressures in the directions along and perpendicular to the magnetic axis,
stable configurations of self-magnetized and magnetized BEC stars are studied
using the recently found $\gamma$-structure equations that describe axially
symmetric objects. The magnetized BEC stars are, in general spheroidal, less
massive and smaller than the non-magnetic ones, being these effects more
relevant at low densities. For the self-magnetized BEC stars their inner
profiles of magnetic field can be computed as a function of the equatorial
radii. The values obtained for the core and surface magnetic fields are in
agreement with those typical of compact objects.
