Our front lawn has an oak planted from a 5 gal nursery pot 8 years ago. Last year, for the first time, it bore fruit, acorns all over the lawn. It didn't bother me until this spring when most of them began to sprout.

For now I am uprooting them by hand. How do I deal with them this fall?

Is there a way to thatch them up every winter?

Nothing much you can do. Same as me with my Maple tree and in the spring tiny maple trees growing all over my garden amongst my perennials coming up. I just grit my teeth and get to it by pulling them all out!

Either rake them up in the fall or chew them up with a mower.