2. Nuttall Oak: This fast growing shade tree, also called red oak or pin oak, is said to be the fastest growing variety of oak, and can provide not only a leafy canopy, but a steady supply of acorns each year, which are devoured by squirrels, deer, and turkeys.3.. Northern Catalpa: The large showy flowers of the catalpa, also known as the cigar tree or the catawba, are an added attraction to having this fast growing shade tree in your yard (and great for bees), but the real magic comes from its thick canopy of large leaves.