A lot probably depends on the amount of infrastructure left standing. In most of history kingdoms/empires would grow to roughly a week's travel time from the capital, since that's an area that can be effectively governed. Anything larger than that needs a strong local government, which eventually causes a separatist movement.

If a nuclear war destroys a large portion of highways and communication equipment, you probably end up with Houston being ruled by one group, Dallas by another and San Antonio forming a government with Austin.