The excited states of some odd nuclei near the β3 stability line have been systematically investigated in terms of the spherical relativistic mean field theory (RMF).The ratio between the valence nucleon root-mean-square (rms) radius and the core rms radius, the separation energy and the density distribution have been deduced as signatures for halo or skin structure.A number of halo nuclei states are predicted.We present the scaling laws of the ratio of valence particle rms radii and square-potential radii versus the scaled separation energies.Furthermore the probability for a valence particle being out of the binding potential has been extracted.Based on these results, we propose a relaxed necessary condition for nuclear halo occurrence.Finally we find that the different size of inert neutron and proton cores may affect the exotic structures.