There is also no need for official governance of what are currently other nations, because then the dominating country may have to extend citizenship and rights. The current system of keeping the weaker countries and citizens in check while not extending citizenship and rights is the more efficient system. If you actually take over then you have the headaches and responsibility of actually running a place that is often filled with (from your perspective) losers and schmucks. You can step in and stop what you really do not want to have them doing without the cost of and problems of taking all the way over.
With MNT, a "Leading Force" will likely emerge if the technology is sponsored by a state, most likely the USA, UK, Israel, Russia, or China, and roughly in that order of diminishing probability, in my opinion. (Other countries mentioned in the comments: France, Germany, Japan, and India.) The desire to take control of world affairs will emerge from the constant risk of a rival developing equivalent capabilities. The first nanofactories will be both impressive (in their exponential qualities and complete automation of manufacturing) and unimpressive (their chemical inflexibility, possible cooling requirements, electricity consumption, limited initial design space, etc.) I predict they will be revolutionary enough that the first model may also be one of the most widely distributed. Unless there are serious restrictions on nanofactory self-replication, a near-exponential flood of nanofactories and nanoproducts will follow, flowing from the first system to cross that adoption tipping point. My assumption is that offense is fundamentally cheaper than defense, and nanofactories will be a great worldwide military equalizer, like guns were the equalizer for individual people in the Wild West.
You get a situation where everyone can effectively get a first-strike kill on basically whoever doesn't have the latest defense technology protecting their entire population. One way to launch such an attack would be through stealth assassin microrobots, like the kind in Dune, but better. People don't like to live in hypoallergenically sealed compartments. So they are often outside, susceptible to anything just floating in silently off the wind. The jet streams provide a natural highway for airborne robots, located only 4-10 miles above the surface. Putting a bunch of constantly flying UAVs into the air over a continental or national area to vaporize every dust speck over millions of cubic miles is really difficult, even with MNT. It's cheaper to send in assassin robots programmed to coast to the ground in cities and military facilities, navigate to humans by heat and sound, and inject them with a lethal dosage of botulinum. To counter that attack, you'd either need huge, self-healing, impenetrable domes around the city, or sufficient robots already on the ground to defend all human beings from the extremely small and camouflaged (as insects) assassin bots. Maybe none of this is an issue and I'm all wrong, but it's just one scenario to throw out there.