I see a call to BMWNA Customer Relations in your future. Do not sign anything at the dealership. In fact, if this were mine, I wouldn't even pick it up.

If it was fine before they "fixed" it, and it now needs a new engine, and it never left their possession; it's their problem.

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12 E70 3.5i xDrive
03 E46 330i ZHP
01 E53 3.0i
98 E36 323is
12 Audi A4 Quattro
79 Triumph Spitfire
73 MGB