Over the next fifty years? I would expect to see a united South America and a united southern Africa, but along the lines of the EU, not the USA. They will primarily be economic and social unions, more than political. Member states will still have strong local autonomy, but a common military and navy, a common currency, and common passports with free travel among its members.
The Arab world may do the same, along with another union among the central Asian countries.
The big changes? China buys Siberia from Russia. First the region south of the Stanovoy Range and west to Lake Baikul. Russia agrees since most of the population speaks Chinese more than Russian anyway. The next round they buy everything east of the Lena River. To the south, they annex Burma through a referendum (who receives some very strong financial incentives also), giving them direct access to the Bay of Bengal.
In response to those moves, India and Bangladesh reunite, possibly with Bhutan and Nepal also, and SE Asia forms its own political union (Thailand, Vietnam, the Philippines, etc, possibly Indonesia and/or Japan as well), but a very messy one.
Europe settles its financial crises, and after its third or fourth constitution, settles on something everyone mostly agrees with.
The USA finally agrees to a civil divorce. The West Coast and the Northeast create the United States of North America with Canada, and the South, the Plains states and the inter-Mountain west forming the United Christian States of America. All minorities and non-Christians move to the USNA. Both sides prosper.
Also the Caribbean and Central America for the Union of the Caribbean and Latin America. The University of California - Los Angeles sues for trademark infringement. They lose.
Yet, ironically, perhaps, while the geopolitical map consolidates, local regions and cities get more autonomy than under the current system. Federalism is rejected in favor of subsidiarity. National governments are mostly diplomats dealing with other nations, with little say over domestic policies which are left to individual regions to settle. City councils hold the most power, not national legislatures which are demoted to investigative committees and research services only. They can advise, but no longer dictate.
Also, the biggest political change will be that governments compete to see who can deliver the highest HDI and standard of living at the lowest cost (in energy/resource terms) than striving to have the highest GDP or biggest baddest army. 30 hour work weeks and two month vacations become standard since most work is automated. Robots are common place. World GDP stabilizes around $20K per capita. People spend most of their time on cultural activities than economic.