The piratebay hosts no content and even the torrent files themselves are all served from other users. That's the technical side whether that has any legal bearing is a different question.
In the US, abiding by any DMCA takedown notices is enough to be fairly certain you are not going to be in trouble for contributory infringement. That's how Google covers itself.
[1] I'm sure copyright holders benefited more than suffered from this free advertisement of love but anyway.