  We study weakly-bound deformed nuclei based on the coordinate-space Skyrme
Hartree-Fock-Bogoliubov approach, in which a large box is employed for treating
the continuum and surface diffuseness. Approaching the limit of core-halo
deformation decoupling, calculations found an exotic "egg"-like structure
consisting of a spherical core plus a prolate halo in $^{38}$Ne, in which the
resonant continuum plays an essential role. Generally the halo probability and
the decoupling effect in heavy nuclei are reduced compared to light nuclei, due
to denser level densities around Fermi surfaces. However, deformed halos in
medium-mass nuclei are possible with sparse levels of negative parity, for
example, in $^{110}$Ge. The surface deformations of pairing density
distributions are also influenced by the decoupling effect and are sensitive to
the effective pairing Hamiltonian.
