The Paul is dead thing was a stunt, a practical joke for a college campus newspaper that went completely out of control. More in the second half of this post.
The 'forensic analysis' of Faul by Carlesi (that gave the conspiracy further legs), ended up being delegitimised. I wrecked it myself with my own facial recognition analysis. The idea that Paul is dead is, as Mike said, bats**t crazy, for the simple reason that it doesn't have a single leg to stand on.