  Models of rotating relativistic stars with a toroidal magnetic field have
been computed for a sample of eight equations of state of cold dense matter.
Non-rotating models admit important levels of magnetization and quadrupole
distortion accompanied by a seemingly unlimited growth in size. Rotating models
reach the mass-shedding limit at smaller angular velocities than in the
non-magnetized case according to the larger circumferential equatorial radius
induced by the magnetic field. Moreover, they can be classified as
prolate-prolate, oblate-prolate, or oblate-oblate with respect to surface
deformation and quadrupole distortion. Simple expressions for surface and
quadrupole deformation are provided that are valid up to magnetar field
strengths and rapid rotation.
