This doesn't appear to be as simple as I may have been thinking. IRS Pub 527 page 8 at https://www.irs.gov/pub/irs-pdf/p527.pdf in the first column states:
Basis Other Than Cost
You can’t use cost as a basis for property that you received:
• In return for services you performed;
• In an exchange for other property;
• As a gift;
• From your spouse, or from your former
spouse as the result of a divorce; or
• As an inheritance.
If you received property in one of these ways, see Pub. 551 for information on how to figure your basis.
I go to IRS Pub 551 at https://www.irs.gov/pub/irs-pdf/p551.pdf page 9 and start reading from "Property received as a Gift".
Now I don't see anything for gift rental property or business property. So it appears that depreciation is not addressed. The way I read it, a new cost basis is established and the recipient of the gifted property starts all over with depreciation based on the newly established cost basis. I'm not 100% positive, but it would also appear that the process of figuring the new cost basis includes subtracting all prior depreciation already taken by the giver of the gift.
