I had an Asimina triloba in my garden for several years and it did finally fruit, which was lovely and tasty. However, I am making this post to enlighten those of you who are thinking of planting one in a residential garden. In my garden the parent tree started to send up babies and they were quite aggressive. In the end I decided to cut the Pawpaw down as in a smallish residential garden it was taking up a lot of real estate, so to speak. Since I cut it down and had the stump ground as well, I continue to have tree sprouts, and this is 5 years later. I have heard from others in my area (southern Ontario) that this is a real issue and a problem with these trees.
The article that was in the latest post of NGA waxed on about this tree and nothing was mentioned about this particular trait. I think it should be included in any write up concerning Pawpaws. I know I would have thought twice about planting it in my garden.