That's maybe the biggest question here. The US hands over control of the internet. Ok. Fine. Sounds good on paper. But who gets control? And please don't say "nobody". Like it or not, certain things need to be policied by some entity. The two things that immediately spring into the mind are domain name control and IP address assignation. Pretty much anything where "globally unique" is a key feature will have to have some kind of controlling entity.
And the very LAST thing I could possibly see as beneficial is if that control was handed to certain entities that would all too eagerly take control of it. Namely corporations with an interest in controlling those resources. Can you imagine what it would be like if a for-profit organization takes over certain aspects of the net? Especially the "globally unique" ones? If you thought domain name turf wars have been problematic, you ain't seen nothing yet.
I'm certainly not someone who thinks it's a perfect solution to hand the control of an important resource to a single country. Far from it. If anything, handing it to the EU sounds sensible, considering how much infighting is going on there and how much bickering, the chance that they could use it against the rest of the world is sufficiently small. Ok, I'm kidding. But I guess it is easy to understand how it's hard to find a good governing body for something like this. Who should take over?
The UN? Please. Take a look at how much success they had with world peace and world hunger and ponder how much more important those two things are compared to the internet. Then consider how much success they'd have policying and governing the internet.
A multi-national consortium? Where's the difference to the UN?
The EU? As I said, considering how much in-fighting and bickering is going on there, it probably carries the lowest risk of anything bad happening. But also the lowest chance of ANYTHING happening when something needs to be done. Plus the highest chance that it will eventually be sold off to the highest bidding corporation.
Decentralize it? Good idea on paper, that was essentially the basic idea behind the internet, but it has deviated from that a long while ago. It's very unlikely that this can still fly. Most likely we'll be running into severe problems before long. Especially when certain countries decide it's a good idea to do a few things differently so they can more easily avoid doubleplusungood ideas to reach the plebs.
Who should take control? I can't really think of many good alternatives, but I'm eager to hear suggestions.