Beginner Gardening: Not sure where to post this. Unwanted seedlings., 1 by wgnkiwi

wgnkiwi wrote:
I have the nastiest trees overhanging my property that drops thousands of seeds all year long into my garden. The seeds germinate regardless of whether the soil is bone dry or nice and damp. Unless I keep on top of pulling them out they just take over and become really deep rooted and strong in no time, and the garden just looks a mess. Short of cutting down my neighbours trees and landing in jail, is there anything I can do to prevent these seeds from germinating without spraying a chemical that will kill my own plants? Here's a couple of pictures of the trees and the seedlings. I have no idea what they are.