Your basis would be your original half plus what you paid for the other half. Because you purchased from a related party - in IRS terms- you must keep the depreciation of the related party plus your own. Therefore, all depreciation ever taken still counts.
You will enter the property on your return with the new basis, keep the date originally placed in service, correct the depreciation from prior years when the program asks and continue on.
About Publication 544, Sales and Other Dispositions of Assets has all the details.
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