The internet isn't being transferred, what is happening is that the ICANN org is being handed over to the UN. They deal with the Domain Name Service system of the internet, of DNS. This is vastly different from the entire internet.
What this means is that, simply, if any website is "blocked" by the UN for x or y reason, you will not be able to type in the Domain Name (bitcointalk.org, reddit.com, 4chan.org, etc.) and get access to it, but you CAN type the direct IP of it and gain access to the website.
It can just be used as a measure to stop subjective "hate speech" from being widely accessible, and discourage readers from the extra effort.
That's also not quite true. They control only the handing out of top-level domain groups, not the identification of specific domains, nor the resolving of domains to IP addresses. Your ISP generally controls DNS resolution, but you can set your DNS server to whatever you like. Google's are free, as are many more. Or set your own up.
Also, any changes to the existing rules require a unanimous vote. Everyone gets veto.