Does anyone knows which are these systems that manages paid wifi networks and some hotels and airports?

Even better, would anyone know a open/free project that would do or could be adapted to that end?

The idea is simple, I want to let the network open at physical level so anyone can connect. After connected however, the clients would have access only to a specified page where they can logging in, and doing the necessary validations the router would allow these of those ports (or even everything) for his IP.