How do we report the acquisition of the other half of the property? Again, if I understand correctly, that half starts depreciating anew, like a new purchase. Do we keep treating each half of the property separately on our tax returns?

Yep - you treat it like an additional property acquisition. Add a second building (and it's associated non-depreciable land) to your depreciation schedule, with an acquisition date of the date you complete the purchase.

However, you can treat the ordinary income and expenses as a single property. You'd just have two assets on the depreciation schedule for the building. So it takes just one column on your schedule E.

I'd guess that you tell TT that you acquired an additional asset for the property that needs to be depreciated. But I'm not a TT user, so I really have no idea how to do that exactly.

--Peter