First let me link my post on how to grow paw paw's: Growing Paw Paws
I don't wish to create an argument with other members, but I disagree that paw paws are a true under story tree. They require protection from Southern sun for the first two years (maybe three is they were from seed in poor soil.)
Full sun and plenty of it, is the correct growing conditions for 4+ year old trees. Paws are spindly and weak if grow in semi-shady conditions in maturity.
There is a dramatic difference between shade-grow trees and full sun trees after 6 years.
Sun grown paw paw trees take on a pyramid shape with extremely dense branching and foliage, you can't see through them they are beautiful and full and look very tropical.
Shade grown paw paws are spindly and thin, with little foliage and most of that at the top of the tree.
A mature sun-grown paw paw can produce 50 fruits at six years and more and larger fruit at eight years, a shade grow tree, at six, will be lucky to produce a dozen fruits, and I wouldn't be surprised at only 5-6 fruits.
Some caveats ... I am in zone 6b (just on the edge of 6a) and more southerly trees will receive more and hotter sun, so may require an extra year of shade.
Some errors, I've noticed in advice in growing paw paws; first, always use white shade cloth, never black or dark. I use old bed sheets, black cloth will add to the stress of the tree by adding heat, you are trying to reduce the heat for the first two years, use WHITE shade cloth.
Also, do not surround the tree with shade cloth and cut off the wind, block the Southern quadrant only, and leave the rest open, the sapling needs the wind.
The trees do get frost damaged in cold winters, with tips usually dying back 2-4 inches if they see much below -5F for too much time. This really doesn't seem to cause much problem for the tree, there are a lot of buds and the few that die off at the tips don't cause the tree to be misshapen in sun-grown trees. However, I've seen a severe cold spell kill a shade-grown four-year-old tree, to the ground. The massive tap root will allow even a completely top-killed tree to survive, in most cases, but several years of severe winters will kill a shade grown tree, whereas a sun grow tree will thrive under the same conditions.
I noticed, what looked like some japanese beetle damage in the photo's above, that's pretty normal, but the beetles prefer other plants and don't cause a big problem with mature trees. (Although it's common to find them on the trees in the spring.)
I don't argue that paw paws can be a bit of a challenge to grow, they need more effort than typical garden trees. The secret is to keep their "feet" out of standing water, and shade them from Southern sun for their first 2-3 years using white cloth and plenty of ventilation.
A picture of a mature sun-grown paw paw two feet from the end of our asphalt drive way. South is to the right of the image, the driveway is E-W. The trunk is about 8" in diameter:
8yo Paw Paw
This tree has about 80 fruit maturing and is eight years old.
Here is a four year old tree, shaded for the first two years:
4yo Paw Paw
South is directly behind the camera. A sharp-eyed plant person might noticed the Ohio-native passion flower vine growing on the fence. This tree was a "what the hell, I have an extra seed" and received less compost and also competes with our asparagus bed to the left, but still has about 20 fruits maturing, even at this young age. It also received two years of shade with a white sheet over a tomato cage blocking the southern exposure. The bed is raised about 8 inches above grade, which helps keep the surface roots drier in our heavy clay soil.