Ask Mr. Smarty Plants

You should understand that the faster a tree grows, the shorter its life will ordinarily be. They sacrifice durability and strength for the speed in growing.The second thing you need to know is that there is no such thing as roots that go straight down. Well, in taproot trees they grow straight down, but they also grow out 6 to 12 inches from the surface of the ground, and often 2 to 3 times the width of the drip line. In other words, if you're looking for a quick shade tree that won't disturb pavements or other plants with their roots, we're afraid they don't exist. Think about it. If a tall tree had nothing but a long taproot (like a carrot) and no lateral roots, the first thing that would happen is the tree would starve to death. The nutrients and water in soil are mostly in that upper 6 to 12 inches. Second, the tree would be basically top-heavy, and would go right over in the first good wind. Those roots radiating out from the taproot are for balance as well as nutrition.

Carya alba (mockernut hickory) and Carya illinoinensis (pecan) are both native to Texas and have taproots. Both are long-lived but also very slow-growing and difficult to transplant because of their taproots, as well as being susceptible to many insects and diseases. Pinus cembroides (Mexican pinyon) has a moderate growth rate, and taproot, but only grows 15 to 30 feet tall. Pinus ponderosa (ponderosa pine) has a moderate growth rate, and grows 72 to 100 ft. 

You didn't say why you wanted trees with those particular characteristics, but if it has to do with being near paving or sidewalks, and getting quick shade, we would recommend you not plant a tree there.You really can't change the growth habits of a tree, and their roots will interfere with foundations, sidewalks and paving sooner or later.

Pictures of Carya alba (mockernut hickory)

Carya illinoinensis

Pinus cembroides

Pinus ponderosa