Buy Common Paw Paw at Trees-Plants. The Common Paw Paw Tree is a native deciduous tree. This tree can grow to be as tall as 30 feet, and about 15 to 20 feet wide. The Common Paw Paw Tree creates an upright, wide pyramidal silhouette. It has large, dark green leaves that seem to droop at the ends of the branches due to their weight. This gives the Common Paw Paw Tree a unique look, it almost has a wilted look to it. The leaves turn a brilliant yellow color during the fall, and in the springtime the tree is covered in purple flowers.