I would second beenthere's idea about contacting Deere. They can tell you almost everything about who makes what in their line. Also, editors of construction equipment magazines will have an idea of who makes what as well.
But... as a quick overview,
Liebherr makes Deere's larger dozers (for sure the 950C and 1050C) and their track loaders (655CII and 755CII). Under this agreement, Deere takes Liebherr's line exclusively in the NA market and Liebherr consequently cannot market its product under the Liebherr name. It CAN, however, market is L752 Mining dozer, which Deere does not carry on its line. Liebherr track loaders are still sold in the US through Liebherr dealers. Liebherr also makes Deere's smaller wheel loaders (compact models).
http://www.deere.com/en_US/cfd/construction/deere_const/newsroom/liebherr_deere_exclusive_090304.html
Hitachi makes 100% of Deere's excavator line, from mini to the 800C. Deere basically takes the Hitachi line, repaints it, and puts in a Deere engine and Deere logos. I believe all hydraulic and other components are identical on the two. It is a joint venture between Deere and Hitachi -- neither owns the other one. It's almost like saying Deere buys certain others' products and relabels them as its own. (As they did with New Holland skid steers until 1999.)
Bell ADT makes the Deere ADTs.
Timberjack is owned by Deere. Deere produces identical Timberjack green and Deere yellow feller bunchers.
Deere's biggest competitor isn't really defined in all senses. While Cat is the biggest equipment manufacturer in the world, do keep in mind that Deere isn't always directly competiting with Cat. For example, in the past, Deere's excavators were more compared to Komatsu's -- both Hitachi and Komatsu hydraulics were smooth and fast, not so true (always) for Cat's machines. In the skid steer industry, Deere is competing with itself to throw the dirtied image of its 200-series skids (and I think they're doing well, or will be). For most markets, Cat is the most-well known and trusted name out there, so yes, Deere is competing with Cat. In certain areas, Komatsu has stepped up its own line and Deere has to compete heavily with them. As far as ag goes, I think it's really come down to a red versus green match, with blue idling (and doing well) somewhere in the background. (That's unsubstantiated btw.)
