  The aim of this work is to extend the deformed relativistic
Hartree-Bogoliubov theory in continuum (DRHBc) based on the point-coupling
density functionals to odd-$A$ and odd-odd nuclei and examine its applicability
by taking odd-$A$ Nd isotopes as examples. In the DRHBc theory, the densities
and potentials with axial deformation are expanded in terms of Legendre
polynomials, and the relativistic Hartree-Bogoliubov equations are solved in a
Dirac Woods-Saxon basis to include the continuum effects. For an odd-$A$ or
odd-odd nucleus, the blocking effect of unpaired nucleon(s) is taken into
account with the equal filling approximation. To determine its ground state, an
automatic blocking procedure is adopted, in which the orbital with the lowest
quasiparticle energy is blocked during the iteration. This procedure is
justified by comparing with the results from the orbital-fixed blocking
calculations, in which the blocked orbital near the Fermi surface is fixed
during the iteration. The ground states for both light and heavy nuclei can be
provided by the automatic blocking procedure as the orbital-fixed blocking
procedure, but with considerably reduced computational cost. The numerical
details for even-even nuclei are found to be valid for odd-$A$ and odd-odd
nuclei as well. Taking Nd isotopes including both even-even and odd-$A$ ones as
examples, the calculated ground-state properties with PC-PK1 are in good
agreement with the available experimental data. This work paves the way to
construct the DRHBc mass table including all even-even, odd-$A$ and odd-odd
nuclei in the nuclear chart.
