The Aztecs either conquered or required the other city states in that area to pay taxes to remain somewhat independent. The capitol of Tenochtitlan became Mexico city which the Spanish ruled out of giving the Aztecs more contemporary importance in Europe, it was also the largest city in the Americas for a period of time. In addition to this many of the written records of Aztec culture that is written by the natives themselves comes out of Mexico City and is in the language that the Aztec spoke.

The books Empires: Perspectives from Archaeology and History by Alcock has a great chapter on the rise and dominance of the Aztecs before the Spanish.

Aztecs Under Spanish Rule by Gibson explains the changes that happened in the Aztec empire and Mexico City after the conquest and it gives you a good picture of how the Spanish used the already existing Aztec tribute system (among other Aztec governing policies) to exert control over Mexico.