What is this plant, and maybe more importantly, how big could it get? I like the large leaves (they're approx 18" wide) but will have to cut it down if it plans to get too large.
This appears to be Paulownia tomentosa, the empress tree. It is an ornamental tree that has become an invasive weed tree in many areas. They can grow very fast when young.
They can reach over 80' in height, but more commonly, 30-40 feet.