Prior to the constitutional convention, what two models of intergovernmental relations predominated throughout the world?

Governments typically had been either unitary or confederated.  Or another way to say that is that they either focused on centralized power (in someone like a king) or particularized power -- the power in the parts of a kingdom rather than at the center.

So, for instance, in France (prior to its Revolution), all the power in the kingdom centered in the hands of the king.  For 175 years, they didn't even have a meeting of the Estates General which was their version of a representative body.  And the power of nobles on their lands was reduced while the king's power grew.

Meanwhile, in the German territories, there was a loose confederation called the Holy Roman Empire.  One of the kings or princes held the title of "emperor," but he really had no imperial power.  The confederated German states retained control over their own kingdoms or territories.

The American experiment mixed something of the best of both approaches. There would be strong central power in the federal government, but putting checks and balances on that power by retaining certain aspects of control in the hands of the states within the union.

It was a combination of conquests and alliances