  The variation of the size of two-body objects is investigated, as the
separation energy approaches zero, with both long range potentials and short
range potentials having a repulsive core. It is shown that long range
potentials can also give rise to very extended systems. The asymptotic laws
derived for states with angular momentum l=1,2 differ from the ones obtained
with short range potentials. The sensitivity of the asymptotic laws on the
shape and length of short range potentials defined by two and three parameters
is studied. These ideas as well as the transition from the short to the long
range regime for the l=0 case are illustrated using the Kratzer potential.
