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Legally...how much of the car do you have to transfer (by percent or specific parts) to be legal?
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You can sell any or all of the car and it's not a problem. Most State laws make it a crime to sell a VIN tag though, even with an accompanying title. The crime comes into play when you take the tag from one vehicle and place it on another. Heck, you can even take the VIN tag of one of those infamous missing ZL-1s and dance in the streets with it

but if you try to rivet it onto another car it then becomes a Federal Felony. The added bonus (to the Feds) is that the car is now deemed "contraband" and will be seized. Once declared contraband it cannot be sold at one of those government auctions either. It usually gets used as a government car in some manner or another or is crushed..... I can just see it now, Efram Zimblist, Jr. cruising up to FBI headquarters in his seized, rebodied 69 ZL1.