All I know is that pumpkins are the easiest thing in the world to grow, given the right conditions and it sounds like you have the right conditions. It WILL take over your yard (they can spread as much as 12 feet in either direction but they don't usually cover a circular area) and if you want pumpkins, you have to let it grow as big as it wants, because the pumpkins are produced out on the stems. If you want just one pumpkin, you can break off any babies that form, or break off the flowers before they open. If the plant just bears one pumpkin, it will put a lot of energy into it, so it will be a large one.
I grew enough pumpkins for our (large!) extended family on two pumpkin vines one year. They're fun to grow.