  We investigate theoretically the long-range electrostatic interactions
between a ground-state homonuclear alkali-metal dimer and an excited
alkali-metal atom taking into account its fine-structure. The interaction
involves the combination of first-order quadrupole-quadrupole and second-order
dipole-dipole effects. Depending on the considered species, the atomic
spin-orbit may be comparable to the atom-molecule electrostatic energy and to
the dimer rotational structure. Here we extend our general description in the
framework of the second-order degenerate perturbation theory [M. Lepers and O.
Dulieu, Eur. Phys. J. D, 2011] to various regimes induced by the magnitude of
the atomic spin-orbit. A complex dynamics of the atom-molecule may take place
at large distances, which may have consequences for the search for an universal
model of ultracold inelastic collisions as proposed for instance in [Z.
Idziaszek and P. S. Julienne, Phys. Rev. Lett. \textbf{104}, 113202 (2010)].
