Ask Mr. Smarty Plants

You did not say which holly was being grown in Arizona, We checked in our Native Plant Database for all the Ilex (holly) genus that grow natively in Arizona and found there are none. That may be the first clue; plants that produce sprouts coming up from their roots are often stressed by environmental conditions and just trying to put out some survivors to carry on when the main plant dies. Growing in conditions hostile, or at least non-native, to a plant can certainly produce stress in that plant.

There is one plant with "holly" in its common name, Atriplex hymenelytra (Desert holly), that is native to Arizona. However, it is not a true holly although this USDA Plant Profile does show it as native to the Surprise area. You could follow the plant link and see if this looks like the plant your friends have in their yard.

Nativity aside, if the house is not being lived in year-round and watering is not being done in the hot weather, the plant is just trying to get some leaves out on those sprouts to help survival if the leaves on the shrub proper shrivel up and die. About the only treatment for the sprouts is to cut them off, and keep cutting them off, near their base. You can't use a poison on the sprouts because they share the roots of the bush for nutrients and water. We are afraid that the choice of that plant for those particular circumstances probably have doomed it. We realize the plant was probably purchased locally, on the assumption that if it was sold there, it would thrive there. Unfortunately, too often this is not the case.

From our Native Plant Image Gallery:

Atriplex hymenelytra

Atriplex hymenelytra