legumes next to GMO corn field

So I just bought 8 acres of beautiful south dakota ground and my first mission is to plant windbreak all around the pasture. Im right in the middle of factory farmed corn/beans with lots of spray and lots of nitrogen that I obviously want to keep at bay. But one thing has me wondering, what is the effect of my nitrogen fixing plants next to all that corn? It should supply my neighbors crops with some extra N but are there any downsides for me?

Does nitrogen fixing travel that far, or is it pretty localized around the roots of the nitrogen fixing plants?

My guestimate is that applied fertilizers are like a huge shot of nutrients, so much so that much of it goes unused and is washed away. But I would imagine that any N fixers put out a sustained level of N that could be utilized immediately, effectively giving your plants *more* nitrogen than by fertilizing (unless you fertilized near constantly). And I would second Rebeccas question/suggestion that any remaining N would not get far beyond the root structure of your legumes before being utilized. I would be much more concerned about stuff coming the other way.

I would think your biggest risk is that the corn is Roundup Ready and that they hose everything down with Roundup regularly to control "weeds". My concern is that it would end up "controlling" anything you're trying to grow as well. That and you might not be able to save seed from any corn/beans/whatever else you're growing. That said, it all depends on exactly what "spray" means.

I think your best starting point is to have a friendly visit with each of your direct neighbors and ask them (politely) about their methods - especially if there are ones uphill from your property. Then, once you know what's going on, you can try to mitigate from there if necessary.

Fertilizer is too expensive to waste anymore so they are much more careful not to use too much.

Roundup isn't cheap, either, so most are careful to only get it on their own plants. Does the grass still grow in the fenceline or ditch? That is a good indicator of how far they overspray.

But spray drift would be my bigger concern. Sprays can drift through the air and kill trees a LONG ways downwind. When it is hot some chemicals will volatilize and drift with the wind days after it was sprayed.