Available in 3 gallon, 7 gallon, 15 gallon and 25 gallon sizes. Scientific Name of Archontophoenix alexandrae (ahr-kont'-o-FEE-nix a-lek-ZAN-dree). The Alexander Palm Tree is endemic to the rain forest of the northern and central coasts of Queensland, Australia.. Also known as the Alexandra King Palm, Alexandra Palm and the Alex Palm. These trees can grow up to 80 feet high with a 1-foot diameter and are considered quick growers. In the right climate, Alexander Palm trees can add 1 or more feet annually to its trunk. The Alexander Palm requires a rich, humus-laden and well-drained soil. They can withstand freezing weather over 26-28 degree Fahrenheit.