Rosemary is native to the Mediterranean, and adapted to desert climates. For Tucson and Green Valley areas, Rosemary can work either as a shrub, ground cover while doubling as an herb for cooking. Not all Rosemary species, however, taste the same. Some are way too piney tasting to work in cooking.
Trailing Rosemary, Rosmarinus officinialis, is a tough ground cover and is suitable for using in recipes. This species reaches about 16 inches tall, spreading up to 4 to 6 feet. This is a good choice for spilling over rock walls, or to reduce erosion on a steep bank. This makes a nice addition in a sunnier part of your herb garden.
Trailing Rosemary blooms in late winter. The blue flowers are not fragrant, but bees love them. Rosemary needs excellent drainage, and will rot out if over watered. Yellowing of the leaves usually means the plant is not receiving enough water.
Reference: Mountain States Wholesale Nursery and Gregg Starr Nursery Plant Info Sheet, 1999.