Question: What is the best fast-growing shade tree?
Answer: There is no good, fast-growing shade tree. Speedy growth is a very poor criterion for choosing a shade tree. Durability, attractiveness, pest-resistance and property value appreciation are all far more important. All racehorse trees have some type of fatal flaw, whether it's insects, diseases, weak wood or bad form. Trees such as willows, cottonwoods, catalpas, Siberian elms, Arizona ash, silver maples, Chinese tallows, boxelders, sycamores, fruitless mulberries, purple plums and mimosas all have very short life expectancies. You're far better off planting a moderate-growing tree and caring for it regularly. Best candidates for most of Texas include cedar elms, live oaks, Shumard red oaks, chinquapin oaks and bur oaks, also pecans and even Chinese pistachios.
On a related note: beware of Sunday supplement and other advertising touting the virtues of any fast-growing shade tree. Invariably these are of the same poor quality as all the others just listed. Most often they will be relatives of cottonwoods, willows and catalpas.