Ask Mr. Smarty Plants

A mature Diospyros texana (Texas persimmon)  ranges in size from 12 to 36' tall, which means you already have a pretty mature plant. The Texas persimmon is evergreen in USDA Hardiness Zones above Zone 8, so in Angleton, which is Zone 9, the tree should still have foliage on it. Nevertheless, at this time of year, it is at least somewhat dormant, so right now would be a good time to transplant it.

First, prepare the hole you are going to transplant into. Do not dig up the tree until you have completed the preparation of the hole; you don't want the roots to dry out. The persimmon likes full sun, but can tolerate a little light shade. It is drought resistant, but needs very good drainage in the soil. We recommend choosing a good spot and digging a hole bigger than you think you will need.  Mix some compost or other organic material with the native dirt. This will help to make nutrients available to the roots and keep them from standing in water, as the amended dirt will have better drainage. 

The persimmon is rhizomatous, which means it has horizontal roots from which shoots grow up and roots grow down. Although our Native Plant Database names seeds as the propagation method, these rhizomes or roots also spread the tree, sometimes forming thickets. This About.com:Landscape article on Transplanting Trees and Shrubs gives good instructions for deciding on rootball size, cutting through roots that are beyond what you can manage, and transportation to the prepared hole. Because of its semi-dormancy and the rhizomes that make up its root system, it should be able to withstand this without too much damage. Once you have returned the amended soil to the hole and your tree is either supporting itself or staked upright, stick a hose in the soil and let water drip in slowly until water stands on the surface. If there is regular rainfall, you shouldn't have to repeat this more than once a week or so. 

If the tree begins to show signs of stress, like wilting or loss of leaves, trim off about 1/4 to 1/3 of the foliage to compensate for the root loss below the ground. Make sure it is getting plenty of moisture. It can take up to 12 months for a tree to fully recover from transplanting, so be patient.