  Very weakly bound systems may manifest intriguing "universal" properties,
independent of the specific interaction which keeps the system bound. An
interesting example is given by relations between the size of the system and
the separation energy, or scaling laws. So far, scaling laws have been
investigated for short-range and long-range (repulsive) potentials. We report
here on scaling laws for weakly bound two-body systems valid for a larger class
of potentials, i.e. short-range potentials having a repulsive core and
long-range attractive potentials. We emphasize analogies and differences
between the short- and the long-range case. In particular, we show that the
emergence of halos is a threshold phenomenon which can arise when the system is
bound not only by short-range interactions but also by long-range ones, and
this for any value of the orbital angular momentum $\ell$. These results
enlarge the image of halo systems we are accustomed to.
