Like, a mining company produces steel, that is used to produce mining trucks, that is used by the mining company. Factories produce silicon, that are used to make solar panels and chips, for power and computing for the AI-run mining trucks. And at the root, AIs run everything, just trading money back and forth to buy the things they need and keep working.
It's just a human economy, with the humans gone. Pointless economic activity.
The question is, what's the path from here to there? Well, it probably looks like a multipolar trap, where every company has an incentive to automate more. Humans try to stop or slow it down, but companies with more AI can hire more lobbyists and get things done. AIs are smart enough to think of all the things that could slow their business down, and get rid of obstacles in the same way humans do. There are probably still lots of small, inefficient human owned businesses, but fewer and fewer over time. (We've seen this trend for a while already!)
I'm hoping a massive backlash would stop this -- but if it's coupled with short-term increases in living standards for people, I think it would have a lot of support, until things start to go really bad, but by then it might be too late, if AIs have control over news media and telecommunications and can stop dissenting humans from coordinating any sort of rebellion.