I have a large live oak in my yard and have a problem with small trees trying to grow that have sprouted from acorns. They are so thick that they have about killed the San Augustine. What can I do other than continue to mow them. Is there a broadleaf weedkiller that is safe to use without harming the tree? Thanks.

A certain small percentage of live oaks and Yaupons have this problem. It may be from the acorns as you suggest but I think it might be otherwise. Scrap the dirt away from some of them and see if they are attached to the roots of the mother tree. If so, there is no quick way to get rid of them. Any spray that is toxic enough to kill them will kill the mother tree.
Tony M

There's no such thing as a braodleaf killer that won't hurt your tree eventually.

With baby oaks, I just pull them if they're in a planting bed, or mow them when they're in the lawn. There really won't be a problem doing it that way.

Tony has a good idea, though, to verify these are form acorn, not from the ends of roots trying to start a new tree.

_________________
Shepherd of the Trees
It is not our part to master all the tides of the world, but to do what is in us for the succor of those years wherein we are set, uprooting the evil in the fields we know so that those who live after may have clean earth to till.

They are not from acorns. Most Q. virginiana aren't especially var. fusiformis.

That is the tree itself adventiciously sprouting new growth.

Poison that, you poisoned your tree. I don't like the term "parent tree" that implies the 2 aren't the same organism with a common vascular system.

Mow 'em, most people do.