What is the maximum number of branches on one circuit?
No, and also, no. But perhaps a qualified yes.

No limit on number of junctions/branches per circuit, unless it's been added at the local level. And even then, reports I've seen here of inspectors with some number of end-use boxes in mind as a limit don't care if the boxes are all in a line or madly branched every which way.

But you will soon run out of available power to run devices at the same time; Or you won't meet required VA per square foot requirements; Or, you will be lacking adequate overcurrent protection.

Of course, if you care to modify your interpretation to include the breaker boxes along the way that DO provide the current limiting, "adding breaker boxes and junction boxes to one main line of power" is exactly what your house and even neighborhood power system looks like. There just happen to be a larger number of branches at a few breaker boxes to deal with the overcurrent protection.