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Tree of heaven (Ailanthus altissima)
An incredibly fast growing tree here in the South-Eastern U.S. (Specifically Kentucky). This tree has both the appearance and function of an emergent palm in our deciduous forest, jumping up to gaps in the over story faster than any native tree can manage (even tulip poplar can't compete!) This would be a beneficial attribute (contributing diversity to the local ecosystem) if not for its tendency to take over large areas very quickly (especially after any form of logging, with the largest groves forming after clear cutting).
The wood is similar in quality to Ash, and can be utilized accordingly. I have had great success with using it as a border for raised garden beds. It is fairly strong and can be used for pole construction as long as it stays out of the weather (E.G. on concrete slabs , for interior walls, etc.).
It tends to rot down fairly quickly and can be left where its felled to add a quick shot of organic matter to your forest system.
If cut in winter, the tree will resprout in the spring and, coupled with its extremely fast growth, can be a good source of renewable firewood (one of it's really beneficial properties).
I would definitely advise Against introducing this tree to your property, but if it's already there it can be used to your advantage.