All wild battle pets (those caught by pet battling) come in all 4 qualities (or rarities if you like). There is no list, because they would all be on all 4 lists. There are some vendor/purchased pets that only come in Uncommon. That's the list posted earlier. So those pets would have to have a stone used on them to be any rarity other than uncommon. Then there is a small list of non-battle pets that don't really have a quality because they don't have battle stats (like balloons etc). So they have no "rarity" and wouldn't be on any of the 4 lists you mentioned.
Warcraftpets does have a list about rarity, but it is referring to how many people by percentage have collected a certain pet. It's under the community tab called pet collection stats. Maybe that's what you are looking for? Fun to see if you have a pet that most others don't
Also FYI, there are no epic pets a player can have. The item that teaches the pet may be epic, but the pet will be listed as rare. The only "epic" pets (and even legendary pets) in game are in the tamer battles or beasts of fable which are not capturable by players.
I hope this clears things up. Was there any pet you had a specific question about?