A non-trivial dynamics of the Earth’s population growth in a historical time, viz. inverse power trend from XVI to XXth, and a transfer to fast linear growth in the second half of XXth century, is analyzed. A hypothesis of two limiting stages of the growth is suggested. Up to XXth century the growth was limited by a slow (centennial) process of unification of administrative and economical subunits within national states and regions, whereas the contemporary growth is going in faster, biological time scale (generations) and restricted by social factors. The inverse power, or hyperbolic, dynamics displays close similarities with phase transitions, like condensation or crystallization in physical systems. The latter are characterized by inverse power distributions of domains’ size in transforming phases that gives rise to hyperbolic relation of measurable critical parameters of a system with a control parameter.