Big papayas bought in markets grow on cultivated trees developed horticulturally from Wild Papaya trees, Carica papaya, which are native to the American tropics. In fact, Wild Papaya trees are among the most eye-catching species along many of the Yucatan's roads (not in the arid northwest) because they are so unlike other trees with their big, umbrella-like leaves arising atop thick, succulent, mostly unbranched trunks. Two Wild Papaya trees are shown below.
In that picture notice that flowers on the tree at the left grow at the end of long, branched stems. That tree is male. Flowers on the tree at the right arise directly from the trunk, and that tree is female. On the female tree at the right the fruits -- the papayas -- are about the size of golf balls. On wild trees that's about as large as they get. When they turn orange they'll be edible and the flesh will taste OK, but there won't be enough of it for most people to bother with. Birds, though, especially woodpeckers, love eating them. In fact, usually it's hard to find a mature, orange Wild Papaya fruit that doesn't have a hole in it from where some critter has been eating it.