Pauly D -- Can't Hide Love For His Baby Girl

Parenthood has clearly not cramped Pauly D's style .... he happily strolled out of Bootsy Bellows nightclub in West Hollywood late last night ... but there's no doubt -- being a father is front and center in his brain.

Check out the video ... it's not so much what Pauly says -- we know he's fighting for full custody and it's nasty -- but you can see and hear how much he loves his kid.

It's pretty rare when celebs come off so real and unfiltered.