A peer-to-peer collaboration system in which changes to a shared space may be broadcast to all of the peers in a collaboration session using messages sent with a combination of addressing techniques. Messages may be addressed for direct peer-to-peer transmission, indirect transmission through another peer or indirect transmission through a server. The type of addressing used to communicate with each peer is determined through the use of a routing table. The routing table defines interconnected groups of peers and may be used to select one or more peers in each group as the initial recipients of the message. The initial recipients may forward the message to other peers within their groups, such that all peers receive the message. For peers behind a NAT, one or more NAT traversal techniques may be used to obtain information to construct the routing table.