I'll just copy what I wrote in a similar thread, and add... GOOD LUCK!!

I've told this story several times- I had two ancient Paulownia tomentosas removed from the front yard of our new house in May of '07- before we even moved in.
I felt terrible that our new neighbor's first impressions of us were as tree killers, but it simply had to be done!
As much as I hate killing a tree, I am not a criminal.
The criminal is the IDIOT THAT PLANTED the damned things.

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- you'd cut them all then the next morning there would be another hundred of them 2 inches tall.

They came up again equally as bad in '08, all spring and summer.

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.

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

AND...
I cut more root shoots in the spring of '11!!!
Four. Full. Years. After the trees were removed.
This tree is the devil!!!

This is the very first year I have not seen one- five full years of diligently patrolling the yard with scissors to cut root shoots.
In a way you're gotta respect that degree of the will to live!