A few years ago our son and daughter-in-law brought us a small tree in a pot at Christmas. It was about a foot tall. They explained that this was a fast growing tree and left us with instructions that involved cutting it and replanting it.
Two years ago we planted it near our swing set. (We don't have swing set age kids, but the previous owners did. And there is always the hope for grandchildren or even random unknown kids to hike up here and swing!) It was 19 inches tall.
Now look at it! Paulownia trees are not only fast growing ornamentals. They are also good for furniture and veneers. The leaves are used in some parts of the world for animal feed. These leaves are huge. Maybe I should give up all thoughts of planting fields of lavender or fruit trees and grow Paulownia. Even with limited knowledge and a whole bunch of neglect, look what we got!