Java APIs

Let's think about a P2P architecture, and say there's no connection between anyone at the moment. How every P2P Client connect to each other? I think we have to have a light-weight server listening on a port waiting for P2P clients, and then direct them to each other. Meaning that the server says to one client(connected to the server) to connect to the another client by giving its ip and port number.

Another question comes if I'm right:
Server IP : 10.10.20.21
Server Listenening port : 1234


#1 client comes to connect,
IP : 10.10.20.45
Port : 1300

when #2 client comes:
IP : 10.10.20.56
Port : 1715

How does the server make them connect to each other? Does it kill the connection between itself and #2, and a method call to number1 giving 10.10.20.56 and 1715 to make it connect to #2? or what?

Is it possible to implement a P2P architecture between peers without having any central server processing?

Thanks.