A: It helped to have a clipping of a stem and leaves of this plant plus to know it grew up as a volunteer in your landscape. At first glance I thought it might have compound leaves, which would have made it easier to identify because only a few trees have compound leaves. However, after searching my native tree books I was able to discover this tree is probably a Sugarberry or Sugar hackberry, Celtis laevigata.
The leaves of the hackberry tree are simple and the leaf base is oblique or uneven, which narrowed the identification field. Sugarberry is a very large, broad, fast growing deciduous North American native tree found in most states of the U.S. except around the Great Lakes region. This light green leaves turn bright yellow in fall and can be showy in some years. The gray-brown to silvery bark has some warty projections or corky ridges, making it attractive in wintertime.
The Sugarberry has a tendency toward trunk rot especially if weed-eater or mower damage occurs. This susceptibility to trunk rot in mature trees is similar to that of a Laurel Oak. Remember it is best to keep lawn grass away from the trunk and roots of trees and shrubs to avoid mechanical damage to the roots and trunk.
Sugarberry will grow in a variety of soil types but grows best in moist, fertile soils in a full sun location, though it will tolerate partial shade. It is sensitive to highly alkaline soils and leaves will show premature yellowing if the soil pH is too high. Sugarberry is moderately drought and salt-tolerant once it is established and is very adaptable, growing in wet sites fairly well.
The tiny, berry-like, sweet fruits attract many birds. Sugarberry should be included in any natural landscape setting and is an under utilized tree. This information was adapted from UF/IFAS publication by Dr. Ed Gilman & the US Forestry Service: http://hort.ufl.edu/trees/CELLAEA.pdf