Central-Leader Form
One principal, or central trunk, also called a leader. This is perhaps the most notable traditional form. It’s also, one of the most efficient forms for the home grower. The single rising leader creates apical dominance, where all the other branches are encouraged to spread out, not up… and grow in essence, to support the tree.
With a central-leader tree shape, you keep the lower section of the trunk (roughly below 36″) free of branches. This is also known as the pyramid or Christmas tree shape… While it’s a bit hard to see in a lush, older tree… the idea is that the lowest branches are widest and get smaller as you move up the tree.
You want a minimum of 8-12″ between scaffold branches. And these branches should alternate direction as you move up the trunk of the tree. As much as 24″ between main scaffold branches is fine as this allows ample room for the branch to fill out as the tree matures.
The primary disadvantage with Central-Leader form is that it maximizes tree height. This makes working the upper portion of the tree, and harvesting upper apples more of a challenge.
Open-Leader Form (Open Center/Vase Form) 
The other primary apple tree form is known as the open-leader, open-center, vase form.
This is where you head the young tree back to around 30,” encouraging multiple new leaders, usually 3-5, to emerge. (see photo right) These new leaders establish a codominance relationship, where no one leader is “in charge,” and all the resources of the tree are shared equally (more or less).
Without any upright growth in the trees center, this allows the most light and airflow through the tree. This in turn promotes the ripening of apples as well as help minimize disease issues.
Unfortunately, while popular, this form has the distinct disadvantage in that it creates a weak union at the single point where all the leaders emerge.
Open-leader trees are far more prone to splitting and/or receiving irreparable damage at some point during maturity.
Modified-Leader Form 
A highly successful approach for the home grower, is the modified-leader form. This is a hybrid style of the first two.
Here, the tree is again headed back at a young age, maybe not quite as low as in the open-leader form.
But instead of allowing multiple new leaders to leap off in every direction where the heading cut is made, a single new leader is established. Your 3-5 strong secondary scaffold branches are then allowed to grow anywhere along the upper portion of the main trunk, as well as along the new leader. In the photo to the left, we can see four distinct leaders.
In fact, while the modified-leader form does have a single new continuation of the main trunk, the strong scaffolding branches are allowed/encouraged to grow as much as (or nearly as much as) the new main leader. In essence this creates another codominance environment, like the open-leader form.
A modified-leader tree no longer holds the pyramid shape of the central-leader form. While the center of the tree is opened up a bit due to the offset position of the new leader, the center is not fully opened like an open-leader form.
The new leader of this form does shade out the center of the tree a bit. Which can be a benefit when growing trees in hot southern summer locations. The remaining leaders spread out, while retaining maximum strength on the main trunk. Again, it’s kind of combining the best of both worlds of the other forms.
Modified-Open Leader Form
If you want to use an open-leader form, we recommend considering a modified-open leader form.
For this form, you head the tree back, again a bit taller than the standard open-leader form and work to establish a number of primary scaffolding branches with enough space between them, before heading back the leader with a final cut.
In essence, this is the same concept of the open-leader form, except that you’re making sure the multiple new leaders begin with adequate vertical space between them on the tree (addressing the main flaw of the core open-leader form).
It’s also a very similar form to the modified-leader form, with the difference being, here, you do not allow the main new leader to continue. Once your main scaffolding branches are established, you cut back and prevent the center growing leader from progressing any further.
Espalier Form
Reserved primarily for dwarf trees, espalier form is a flat, two-dimensional tree shape against a trellis or wall. Trees shaped to an espalier form have an upright trunk and multiple horizontal branches on each side. This is perhaps the easiest form to maintain and harvest… once it’s established.
But we don’t sell dwarf trees, so we’re not gonna speak much on this one.