The Passuk in Bereishis 15:9, describing the opening of the Bris Bein Habesarim says:
קחה לי עגלה משולשת ועז משולשת ואיל משולש ותור וגוזל.
There are a boatload of opinions on what Meshuleshes and Meshulash mean (3 years old, 3 of them, a 3rd born, a fatty one etc. etc.), however, I had always understood it to mean that it was an animal cut into 3 pieces. I have not been able to find this Peshat anywhere though, which really bothers me, as that likely means there is something clearly wrong with it, but I can't figure out for the life of me what that is!
It fits very well for a number of reasons. Firstly, we have similar words meaning the same thing (see Devarim 19:3), it would explain why Avram cut the animals and not the birds. It would explain why he knew to cut them without Hashem telling him. It would also explain why the word pieces and not halves is used in the continuation.
So I'm looking for a source that mentions this Peshat, and/or something that would disqualify it directly.
Edit: I spent a while researching it last night myself, and I think I may have an answer, but I really don't like it, so I'd like to see what others come up with first.
Edit: Thanks to mevaqesh for suggesting that I make a list of all commentaries I have checked, even if they do not comment here or on this in specific point. While I don't remember all of them, I'll start a list (in no particular order): Targum Onkelos, Targum Pseudo-Yonasan, Targum Yerushalmi, Rasag, Rashi, Ri Kara, Rashbam, Ibn Ezra, Bechor Shor, Chizkuni, Radak, Ramban, Ibn Caspi, Seforno, Kli Yakar, Kesav VehaKabbalah, Malbim, Netziv, RDZ Hoffman, Abarbanel, Rabbeinu B..., Or Hachaim, Alshich, R' Chaim Paltiel, Daas and Hadar Zekeinim, R' Hirsch, Mendelssohn, Reggio, Professor Artom, Living Torah, various Christians/Christian translations, etc.