Ailanthus altissima.

Here is a link that might be useful: Ailanthus altissima

You might want to read up on your Ailanthus before babying it too much longer. ;-)

Here is a link that might be useful: check this out!

I second rhizo - stop babying this tree and get rid of it. FAST.

We had 2 of these in our yard. We cut the small one down - it was about 20' tall - in June 2009. By October 2009, the stump has shot up 2 sprouts, each about 6-7' tall. Here it is, 2 years later, and weekly I go out and cut shoots that are a foot tall. Many shoots are 20 or 30' from the original tree, and we dug the stump out. The biggest reason my husband mows weekly is to take care of the shoots in our grass! Granted these tree sprouts could be coming from all the seed pods the trees generate, but the way they grow so fast, I think they are coming up from roots.

We need to remove the second one, but we need a tree service for that - the tree is easily 60' tall. And already I'm dreading the thought of dealing with all the shoots that will be coming up. Our neighbor has one of these trees - it's on his property, but outside his fence, so "appears" to be on out property. Again it is 60' tall so will require a tree service.

I wouldn't wish these trees on my worst enemy!

Cut stump or frill method is most effective if done correctly.

Here is a link that might be useful: Controlling Undesirable Trees, Shrubs, and Vines in Your Woodland

Hack n Squirt Method

Here is a link that might be useful: Hack n Squirt Method