Abstract The recently developed relativistic-mean-field in complex momentum representation with the functional NL3* was used to explore the exotic properties of neutron-rich Pd, Cd, Te, and Xe isotopes. The results were compared with those obtained using the relativistic Hartree-Bogoliubov (RHB) calculations, and available experimental data. The single-particle levels were obtained for the bound and resonant states. The two neutron separation energies S2n and root mean square (rms) radii, agree with the experimental data. It is shown that a halo structure in the extremely neutron-rich 164-180Te and 164-182Xe, as well as a thick neutron skin in the extremely neutron-rich Pd and Cd isotopes. From the numbers of neutrons (Nλ) and (N0 ) occupying the levels above the Fermi surface and the zero-potential energy level, it was found that pairing correlations play an important role in the formation of halo phenomena. These findings are further supported by investigating S2n, rms radii, occupation probabilities, contributions of single-particle levels to the neutron rms radii, and density distributions. The neutron rms radii increased sharply, obviously deviating from the traditional rule r ∝A1/3, and the density distributions were very diffuse. Finally, the contributions of different single-particle levels to the total neutron density and wavefunction were discussed. It was found that the sudden increase in the neutron rms radii and diffuse density distributions mainly come from the resonant levels with a lower orbital angular momentum near the continuum threshold.