It was P2P sometimes, like if you were running in a university or research institution. When skype got installed in there, it took over the university network

It was P2P sometimes, like if you were running in a university or research institution. When skype got installed in there, it took over the university network and quickly became master node for the whole geographic area. For historic reasons, these organizations used to have many computers on public IP (they got large IP block when internet was created very long ago) and had amazing network connectivity.