None of the classic trees that I know of. All the trees in my yard - Sycamore, live Oak, fruit trees - all re-seed all over the yard - I constantly pull out seedlings.

I have quite a few confederate rose trees, and they don't re-seed. I have no idea why not - they produce copious amounts of seeds, but I've never found a single seedling.

Shoe Tree

Funny, Lou - now, name a tree that helps the O.P. with her question.

Kay,
Every tree I can think of has drawbacks in one form or another and the best way to find a suitable tree for her yard is for her to ask all her questions at different nurseries.(do not ask at only one place)

Lou

Question - why do you want to shade your grass? Are you trying to get rid of it? Grass grows best in full sun. And as far as a tree recommendation goes, there are many that will grow in Central Florida. As Lou mentioned, visit the local nurseries to see what they offer. You will minimize the number of seedlings if you avoid trees that profusely flower and fruit. Have you considered a palm or a grouping of palms?