  Halo phenomena in deformed nuclei are investigated within a deformed
relativistic Hartree Bogoliubov (DRHB) theory. These weakly bound quantum
systems present interesting examples for the study of the interdependence
between the deformation of the core and the particles in the halo.
Contributions of the halo, deformation effects, and large spatial extensions of
these systems are described in a fully self-consistent way by the DRHB
equations in a spherical Woods-Saxon basis with the proper asymptotic behavior
at large distance from the nuclear center. Magnesium and neon isotopes are
studied and detailed results are presented for the deformed neutron-rich and
weakly bound nucleus $^{44}$Mg. The core of this nucleus is prolate, but the
halo has a slightly oblate shape. This indicates a decoupling of the halo
orbitals from the deformation of the core. The generic conditions for the
occurence of this decoupling effects are discussed.
