I fully expect that your own K-1 (not just your ex partner's) is marked as final. Since you paid for that 33% and now own 100% of the property, you'll be entering the property as an entirely new rental property with a new cost basis, and depreciation starts all over from day one, for the next 27.5 years.
Your cost basis on the new property is:
What you paid for your share originally when you purchased it, plus what you paid for the 33% you purchased from the partner. From that total you will subtract the depreciation that *YOU* have already taken on the property while it was in the partnership. This total will be your new cost basis. Add to that any property improvements that "you" paid for. You can not include in the property improvements any that the ex-partner contributed to those improvements.
Enter the property as a new rental property with an in service date no earlier than your closing date on the purchase from the partner. You'll indicate that you purchased this property new.
The depreciation "you" got while it was in the partnership is already reflected/reported on the K-1. The depreciation your ex partner took is theirs to recapture on their own tax return - as you already know, of course.
Now, you will have to document somewhere the depreciation "you" took on the property while it was in the partnership, as you will need to include that amount in your depreciation recapture should you sell the property in the future.
