Tell me a little more about the situation. First, have you already cut the main (mother) tree down or did you just cut it back? Second, are the smaller trees suckers from the roots of the main tree or are they seedlings? Lastly, how big was/is the main tree?

I think with these answers and anything else you feel might be relavent, we can find a solution.

We cut it down level with the ground. it came back..as a matter of fact, we did it several times. The spread is by a little black berry that I am sure the birds also help spread. It is an extremely fast grower and is a pretty tree, that is much to close to the house. I have them come up even under other trees, so they are "very easy to nuture"!

Does this help?

Does the "little black berry" have a hard white bumpy berry core? If so, it's probably a hackberry. They reseed like crazy, so you are probably mostly getting seedlings. If you are still getting sprouts from the original trunk, you can try to kill it. Cut off sprouts from the main trunk, then paint the cut ends with super-strength (I forget the official name) Roundup. Repeat as necessary. For the seedlings, just keep pulling!

When you cut the main trunk down, do so flush with the ground so you can mow over it. Use a power drill to drill holes into the stump near the outer edges just inside the bark. Fill these holes with straight regular, non-diluted, roundup. This should take care of the stump.

As for the seedlings in your flower beds, as amazondoc said, pull them (and the earlier you catch them, the easier it will be to do). If there are no other mother trees around (like in the neighbor's yard, etc.), within a few years, this problem will be gone. For the seedlings in your yard, the lawnmower should take care of those no problem.

If there is another large tree around that is going to produce seeds every year, you may have to use a pre-emergence in your flowerbeds (apply after you have planted any annuals.

Thank you. One of the agriculture reps came to our farm yesterday and he indeed said it was a Hackberry tree..
I appreciate your input. While I will be the first to preserve the forest, there really comes a time when enough is enough. The lawn is not a problem with them. They seem to migrate to my beds and really grow quickly.
Thanks again.
Merriss