Giving some more thought to Facebook: Facebook isn't a monopoly. There are thousands of forums on the net. Facebook is only recognized because of their size and their hold on the social communities around the world. It would be up to each country to determine what is considered detrimental to their citizens. If after a possible warning to Facebook and they don't comply, the country can either sue or cut the cord and stop Facebook from operating in their country.
Breaking Facebook up into smaller companies wouldn't stop the traffic that they broker in. If the government was successful in splitting Facebook up, what have they accomplished? They now have more companies to regulate. Besides, companies would be in line to buy a portion of Facebook and since all the infrastructure is already in place, Facebook's new buyer wouldn't be down for five seconds, just flip a switch.
The last big breakup of a big company was AT&T back in the 80's and that took years. The feds tried regulating them for years and AT&T found a way to get around the regulations or just ignored them. It took almost 20 years to break them up and the lawyers made millions. I can't imagine how long it would take to break up Facebook. One thing the feds might not consider would be how much support would be put in place by the tech community supporting Facebook. It would look like WW3 with ink pens and keyboards and this time, the lawyers would make billions.