if you're driving with an automatic, shutting the car off might not be the best idea. your torque converter which is bolted to the flywheel on the engine is also the pump that circulates transmission fluid through the transmission. with the engine off, the pump is not lubricating your transmission.
think about why when tow companies need to tow a rear wheel drive truck, they don't tow with the rear wheels on the ground unless they disconnect the drive shaft.
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