You depreciate the LOWER of (1) Fair Market Value when YOU made it available as a rental (probably the Gift date), and (2) the Adjusted Cost Basis.
For a Gift, the Adjusted Cost Basis is the LOWER of (1) Fair Market Value on date of Gift, and (2) Your parents' Adjusted Cost Basis (usually purchase price, plus improvement, minus depreciation that they were able to take).
So in most cases, you depreciate your parents' Adjusted Cost Basis, not the Fair Market Value.
