The airplane Rolls Royce company and the motor car one are different. BMW supplied engines to Rolls the car company for a while. Then, when Rolls/Bentley was being sold, BMW stole the name from VW b/c of it's prior relationship. That move impressed Dr. P (however you spell the now retired head of VW) so much, that when Bernd Pietschrieder (yeah, I prolly spelled it wrong) was free, Dr. P asked him to come aboard.
Basically, after it was all said and done, VW got all the Rolls and Bentley plants (no big deal since they were old and needed some serious upgrading) as well as the rights to the Bentley name. BMW just got the rights to the Rolls Royce (just the car company) name and nothing else. They had to build their own Rolls factory. Rolls Royce the airplane engine company still exists independently from either BMW or VW.
Maybach is just Mercedes. Chrysler never had anything to do with it. It was created in response to VW and BMWs moves in buying Bentley and Rolls. Maybach was one of those old, fabulous car companies like Deusenburg that went out of business. I think it was associated with Daimler Benz somehow.
Here's a list of the car companies they own:
VW: VW, Audi, Bentley, Bugatti, Lamborghini, Skoda, I think some Czechoslovakian company, and they're closely linked to Porsche.
BMW: BMW and Mini. I believe they still supply the engines to the Range Rover b/c they used to own Rover before breaking it apart and selling the pieces. Ford now owns the Land Rover company. I think Rover is now held by some group of British investors.
Mercedes: Mercedes, Chrysler, Dodge and close association with Mitsubishi.
Ahh what the hell, I'll throw some other interesting companies in too.
Ford: Ford, Lincoln, Mercury, Jaguar, Land Rover, Aston Martin, good chunk of Mazda
GM: GM, Chevrolet, Oldsmobile and all those other American divisions like Caddy, Daewoo, Saab, Opel, good chunk of Subaru, Isuzu, trying to get out of deal to buy Fiat, some deals with Toyota and Honda
Fiat: Fiat, Alfa Romeo, Ferrari (independent pretty much) which then owns Maserati