That's actually one of the main things that's addressed by this v3 protocol: > Both fragmented and unfragmented messages contain sender and recipient instance

That's actually one of the main things that's addressed by this v3 protocol: > Both fragmented and unfragmented messages contain sender and recipient instance tags. This avoids an issue on IM networks that always relay all messages to all sessions of a client who is logged in multiple times. In this situation, OTR clients can attempt to establish an OTR session indefinitely if there are interleaving messages from each of the sessions. If you've ever tried to have multiple devices logged in to one account using OTR, and you've ended up with an endless spam of "invalid message, resending" or some such, this is what they're talking about. Clients that support v3 properly shouldn't do that anymore, and you should be able to keep both your PC and phone logged in without problems.