...the leaves are wrong for Eucalyptus, which are stiff and leathery, with oil glands. the pic looks much too 'soft' Yeah, not sure of 'softness' or vein color from photo, know next to nothing about Eucalyptus, and haven't been around one for years. Though Googled enough to find it was likely eucalyptus torelliana (now corymbia torelliana) I was reminded of. Here is a link that might be useful: eucalyptus torelliana factsheet

I don't know what it is, but i cut one down on my property. It grew from seed and within two years, it was about 25 feet tall! I have seen them planted in parking lots here and also growing wild (not sure if native or introduced) in the foothills of the Sierra Nevada (Millerton Lake to be more specific).

I posted on your Plant ID forum thread; here is my reply. http://forums2.gardenweb.com/forums/load/namegal/msg0121502231960.html?15 That's probably Red Mulberry (Morus rubra) given the very limited information provided. wgreenlee1 could assist by saying WHERE these plants are growing. From your post here on Trees, I'm going to surmise Missouri - where Red Mulberry would be perfectly at home. I am pretty sure that there are no Tilia sp. with this kind of bark characteristics. It doesn't fit any of the birches either. Not even close on poplar or cottonwood (Populus sp.). Since these plants have been observed by you over a long period of time, I'm certain you would have observed Tilia flowers in passing. You should have seen Mulberry flowers, too - whether male or female. This tree is plenty old to have flowered. Those leaves look large enough, within the range of morphology, and appear coarse enough (along with the written description) to fit right in with Red Mulberry. Lobed leaves are just one expression of Mulberry species leaves, but not the only expression. Your location is significant in answering your question, and additional images of the dormant features like buds, stems, and - be still my heart - the WHOLE tree, make a huge difference in offering lucid opinions to the identity of this tree. Here's an old Red Mulberry trunk for comparison.

They will re-sprout. Cut them near the ground. Use a spade bit (a.k.a. paddle bit) to drill several large holes in the trunk. Fill the holes with Round-up BRUSH killer. Cover with a pot to keep the sun from evaporating the Roundup, to keep birds from drinking and to keep rain from diluting it. Do this about 3 times over the next 3 months. It won't come back and will kill the roots