To be clear, I'm assuming you mean Asimina triloba. If so ...
In Missouri and Nebraska (my
experience) pawpaws are under-story trees growing in riparian zones. This may be what some consider the more "natural" form. In these conditions, the pawpaw trees that I've observed are tall and straight with sparse limbs limiting its
energy to catching dappled sunlight that makes its way through the over
canopy of giant cottonwoods and other river and creek trees. Here's a link to a photo:
http://www.veggiegardeningtips.com/wp-content/uploads/2013/09/Gathering-Pawpaws.jpg
Plant them in the open and they will be shorter and more full and a somewhat conical in shape. They can be trained. Here's a link to a photo:
http://darkroom-cdn.s3.amazonaws.com/2016/09/a9ebfc00fbdf8fd2bb836130d42f855e.jpg
I'd say their form is based on their conditions. I believe there are few pawpaw trees growing naturally in the open in the Midwest of the USA as seedlings don't tolerate direct sun very well and usually burn off the first or second year in direct sunlight. If shaded for the first three or so years, they can survive direct sunlight and will grow more like an orchard tree.
See extensive research by Kentucky State University
http://www.pawpaw.kysu.edu/
People in some communities around the world refer to the papaya as pawpaw, so that's why I generally give the scientific name to remove all confusion.