good question! first, I’d like to plug this book because it’s a really well done demystification of the conquest.
(things labeled ‘dominion’ are independent polities at the time of conquest)
what’s going on here is that the Triple Alliance expands as a hegemonic empire – formal conquest, vassalships, and tribute acquisition coupled with ‘open up The Markets to our merchants or we’ll open up your veins with our knives’. The sphere of political influence that the Aztecs cultivated was more nodal than territorial – some places are important and warrant attention, others just need to be neutral or sufficiently cut-off. cotton and cacao growing regions on the coasts fell into the former, and the latter was both intervening territory and the rhetoric for areas that couldn’t be conquered, like neighboring Tlaxcala. The Mexica famously imposed a cotton embargo against the Tlaxacalan state (also Nahuatl speaking), which meant that their nobles shamefully had to wear maguey fiber clothes like the commoners. The Mexica also sniffled a bit and claimed ‘they didn’t want bullshit tlaxcala anyway’ when the spanish asked why it was independent/so eager to join cortez.
Not pictured on this map is another empire immediately to the west – the Tarascans, a Purepecha speaking polity in the modern state of Michoacán.
The Aztecs desperately wanted the southern portion of this territory for the rich mineral veins (Precolumbian metallurgy is way cool too!) and access to the Pacific but repeatedly got their shit kicked in – a border battle between the Tarascans and Aztecs at Acambaro, Michoacán, was reportedly so devastating that Spanish missionaries still saw skeletons on the ground 80-100 years later. The other *major* polity at the time of the conquest was Tututepec on the coast of Oaxaca, the founding and genealogies of which are the subject of many of the remaining precolumbian codicies.
The Maya area was a series of petty states in the wake of the fall of Mayapan – this is interesting, because it’s the area that actually takes the Spanish the longest time to infiltrate, and even that was by invitation. The conquest of Yucatan is a different trajectory altogether from the central plateau.
at the eve of conquest then, you’ve got three major polities (and a bunch of independent areas that are sometimes claimed for rhetorical purposes) that are receiving tribute from but not necessarily directly administering vast areas of Mexico – all of them are multiethnic, most of their territories are recently acquired, and their tributaries don’t really see a conceptual difference to being claimed by the Spanish vs. the Mexica in the broadest sense, except that the former will let them settle scores against the latter. The narrative of the conquest is different for all of them, and I’m actually delivering a lecture on the Tarascan example next week that I’ll write up for the ‘dp too.Those areas with centralized control and administration were assimilated through both dividing constituent parts for auxiliaries then claiming them as a whole when the overlord surrendered, and for a good 50-150 years in some parts the older systems functioned as they had in the past with tribute obligations going to a different ruler. In this light it’s worth asking the question of how fundamentally different the Conquest was as an event in the history of Mesoamerica – I personally see the late colonial/transition to national period as being the real sea-change.
As far as organizational structure, Mesoamerica appears to have had some constants with ontological divisions into noble and commoner populations, political factions also carrying theological prerogatives (the cult of Huitzilopotchli was the evangelical message of Mexica conquest), and a transition from earlier (Classic period, ~250 CE to 700/900 CE) focal ruler governance to dynastic oligarchies from which leaders were selected (and sometimes deposed) that ruled in a council fashion. I think of Renaissance Italy as my comparative model.