I just finished wiping out the Inca in my game as Spain. They were the dominant civilization on my home continent. I only founded six cities on my home continent, and had no wars there for a long time. I kept 3 divisions as a deterent (that being 4 line units plus one siege per division).
When I got Conquistadors they went sailing with my caravels to find other land masses, and I settled 8 more cities that way. 2 cities on the other major land mass where England, Arabia, and the Iroquois lived. The other six cities on 3 separate unpopulated land masses.
Shortly after settling my two conquistadors near England's territory, I wound up in my first war against Arabia. Arabia had wiped out one civilization there already, and was now attacking England, so I thought I'd help her out. Arabia also used a GA to steal some of my land, and that was not going unpunished. I only had 4 tanks and an artillery on that land mass when I declared war and attacked, and my only avenue of attack was through heavily wooded hills which slowed my tanks to a crawl. Not sure how many turns we fought, but it was constant war from industrial to modern age, and I had only progressed a very small distance. Razed two cities, and puppeted one, but I still had not broken through the rough terrain so I kept having to stop for healing even with a battleship, destroyer, 2 fighters, and a bomber now in the theatre to support my tanks.
Meanwhile, back on my home continent the Inca was wiping out Siam, and controlled probably 2/3 of the land mass. I had to do something about it, so I mobilized my 3 infantry divsions (by this time they were mech infantry and rocket artillery), and 4 fighters and attacked. With much more flat terrain, and clear approaches, I was able to do much more damage in a timelier fashion.
As I was putting the hurt on Inca, Arabia finally asked for peace again, and I decided to accept it so I could also make peace with the 4 city states he was allied with. Then I just had Inca and his 1 city state to deal with. I still had not broken through to Baghdad, which was the first major city after the rough terrain, but I accepted the peace and parked my armor around my one captured city.
My mechanized infantry, jet fighters, and rockety artillery methodically took city after city in the Incan lands, most of which I made puppets because Germany still sits up north with a sizable territory (and he has denounced me). After defeating the Inca, Siam was lucky to survive with a single city, and my Spanish homeland now spans coast to coast over 2/3 of the continent.