  We discuss the Bose-Einstein condensation of relativistic vector charged
particles in a strong external magnetic field in very dense matter, as may be
paired spin-up electrons. We show that for electrons such systems may maintain
self-consistently magnetic fields of order in between the interval
$10^{10}-10^{13}$ Gauss. This could be the origin of large magnetic fields in
some white dwarfs, but may also impose bounds due to the arising of strong
anisotropy in the pressures, which may produce a transverse collapse of the
star.
