The existence of tricoordinated Pd(II) complexes has been a matter of controversy for a long time. The recent X-ray characterization of a family of Pd complexes [PdArXL] allowed to certify the existence of true tricoordinated Pd(II) species. The unique role played by the amido ligand (X = NR₂), among a family of X ligands, was noticed in a previous computational work. Here, the influence of the R substituents at the amide and the nature of the Pd-N_amido bond are theoretically analyzed. The relative stability of d⁸ tricoordinated [PdLAr(NR₂)] complexes versus d⁸ tetracoordinated derivatives as a function of the R substituents is studied by analyzing the two most common ways to fill the vacant coordination site in a tricoordinated complex: solvent coordination (with tetrahydrofuran as solvent), or dimerization giving [(μ-NR₂)₂Pd₂L₂Ar₂]) complexes. The nature of the Pd-N bonding interaction is analyzed using several theoretical schemes as molecular orbitals, QTAIM, ELF and NBO. Each of these schemes suggests that the order of the Pd-N bond in this family of complexes is higher than one. An asymmetric π interaction between the nitrogen lone pair and the LUMO over the tricoordinated Pd center is proposed as an important source of additional stabilization of tricoordinated species provided by amido ligands.