I had two ancient Paulownia's removed from the front yard when we moved into our new house in May of '07. I had the roots ground out as deep as the largest grinder would go. The roots shoots that came up that year were horrendous- one every foot covering the entire yard. It was literally a daily chore to keep up with them.

They came up again equally as bad in '08.

In '09 they slowed down a bit on my property but began seeking new areas as I saw them in neighbor yards as well- not only on the adjoining properties but across the street as well.

Spring of '10- three full years since I had the trees taken out- and I am still getting shoots.
THREE YEARS!
They slowed down considerably but I still cut down one or two every couple of days. They are impossible to pull.

I cut more root shoots this spring!!!
2011
Four.
Full.
Years.
After the trees were removed.

This tree is the devil!!!

I tell you this not to discourage you but to let you know what you could be getting into.
They are one tenacious tree.