What is the best shape for a free standing semi dwarf apple tree in a backyard "open center ", "modified central leader “, or central leader” ?
I lean towards the modified central leader if your yard is smaller -the open center can get pretty sprawly. But if you want to use the space there’s something about the vase (open center) that I like. And you can arrange it so that you can do everything from the ground, which is harder to do with the central leader styles. I believe that it’s generally agreed that central leader prunings make a more efficient use of space.
Semi dwarf apple trees can grow quite large and tall, depending on the variety. Most of the semi draft apple trees at my house are modified central leader except for a Stayman that had fire blight when it was into its second year so bad that I cut the central leader out. Then it grew similar to a modified central leader but with the diameter very large for the first 4 feet with 5 scaffolds at that height with one regrown central leader with greatly reduced diameter. Then I again cut out the reclaimed central leader at about 12 feet. Resulted in a very wide tree.
I did plant a couple of standard grafted trees for the deer that I grew from seed that I left as a central leader trees. They are now 20-25 feet tall. I never really tried to manage them.
My only advice is to be careful with the height at maturity. Determine the desired height and plan from there while shaping it so that with a ladder you can get to its highest point.