[en] 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 hyper-radial 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 hyper-moment are possible. (authors)