Johnny Depp and Vanessa Paradis' relationship has BARLEY snuffed it, but Johnny has allegedly been waving his Johnson at other women for quite some time now!

First we heard whisperings of an Olsen Twin affair, then most recently it was a high-flying, horseback riding love tryst with Rum Diaries costar Amber Heard, and NOW rumor has it Johnny has a very 'special' connection with his publicist Robin Baum!

One insider reveals: “Robin and Johnny spend a lot of time together obviously because of work but their relationship seems to be getting much closer than just business… They travel a lot together for work and get to spend a lot of time together and they definitely have a total flirty vibe between them. I would put money on them having more than just a friendly relationship."

We wonder, Robin, is doing your client good for publicity? Ha! PROBABLY!!

Whatever, Johnny obviously has restless leg peen syndrome and needs to stick it in many a hole for relief…