  The different kinds of behaviour of three-body systems in the weak binding
limit are classified with specific attention to the transition from a true
three-body system to an effective two-body system. For weakly bound Borromean
systems approaching the limit of binding we show that the size-binding energy
relation is an almost universal function of the three s-wave scattering lengths
measured in units of a hyperradial scaling parameter defined as a mass weighted
average of two-body equivalent square well radii. We explain why three-body
halos follow this curve and why systems appearing above reveal two-body
substructures. Three-body quantum halos 2-3 times larger than the limit set by
zero hypermoment are possible.
