The big issues that will be facing us in the future boil down pretty much to what entity will serve as the central focus of our public/political life. I think that the large nation state will not be able to hold itself together without the massive inputs of energy allowed by oil and coal.
In order to tie itself together, the large nation state needs to expend energy to tie the units together economically. The larger the state, the greater the energy usage required. The US, China, and Russia are the main examples of this level of physical size, though you probably could make an argument that Brazil, Indonesia, and Australia may be there too. And let us not forget the EU, they are effectively trying to make a patchwork giant state.
So, when the decline in availability of oil starts to gain serious traction, these states will begin to show strain. The distance from the capital will begin to matter as the state has less and less to offer the outlying districts. Large non-capital cities will begin to assert themselves and regional associations will begin to step to the fore.
I think that you will begin seeing something like the good old "Sagebrush Rebellion" but this time they will be taking steroids. Demands for return of taxes will begin and taxes at the state level will go up. The overall large-scale state will begin to deteriorate and without a large, oil-fueled military to put down the rebellion, the states will start to go their own way. So we will be looking at a repeat of Gaul and Brittannia, Dacia and Illyria.
So don't think that this will just happen here. Russia is a hodgepodge of regions with no great love of Moscow. The Uighurs, Tibetians, and the Coastal Cities aren't that fond of Beijing.
The devolution will probably end up looking like Old Europe. States that are sized appropriate to the energy and population base.