Ask Mr. Smarty Plants

"Honey mesquite plants can sprout from numerous perennial dormant buds located along rhizomes or the upper part of the root....When aboveground growth is damaged or killed, new sprouts arise from the bud zone. If aboveground growth is destroyed or damaged during a dormant period, sprouts arise the following spring and often flower during their first growing season. If aboveground growth is damaged during the wet part of the growing season when root carbohydrate levels are high, plants resprout rapidly but do not flower until the following growing season. If destroyed during the dry portion of the growing season when root carbohydrate levels are low, sprouting is delayed or slow, sometimes for 3 to 5 years."

This ability, plus its tolerance to drought conditions, results in different growth forms and the article recognizes three forms:

"1) a single-stemmed tree reaching 20 to 40 feet (6-12 m) in height, with crooked, drooping branches, 2) an erect, multiple-stemmed bush or small tree, often 10 to 15 feet (3-4.6 m) tall, and 3) a decumbent or running bush found on deep sandy soils."

For your purposes, you are probably most interested in the first growth form and the fastest growth possible. The single-stemmed form will depend on trees that aren't injured and the growth rate will depend on soil type and available moisture.

There are many ranchers out there who would readily agree that mesquite is too rapidly renewable. They have been trying to get rid of it for years!