Using someone else's property: What are the legal risks?

About thirty years ago, my family picked up a little vacation cottage on the coast, right next to this shared yard. Now, technically, the yard wasn't ours—it belonged to someone else—but since the owner was never actually around, we ended up using the space as if it were our own. We used that area for three decades, maybe even longer, thinking it was just part of the routine. Then, out of nowhere, we get hit with a notice saying the lot has been bought by someone else and we need to clear it out immediately. It’s left me wondering: is there any kind of legal principle or adverse possession law in the US where you can actually claim ownership of a property simply because you've been occupying and maintaining it for that long?

Can anyone actually make sense of Section 107, subsection 3, based on subsection 1?
http://www.law.gov/property-rights-act
Basically, I'm trying to figure out what the daily rate is in dollars for using someone else's land.
Has anyone here actually sued someone and gotten a court order for using their property?!
How long did the whole legal mess take... how much was the daily fine... and did they run into trouble with people resisting, or did the local police actually follow the court's orders?

Austin Cook74 said:Can anyone actually make sense of Section 107, subsection 3, based on subsection 1?
http://www.law.gov/property-rights-act
Basically, I'm trying to figure out what the daily rate is in dollars for using someone else's land.
Has anyone here actually sued someone and gotten a court order for using their property?!
How long did the whole legal mess take... how much was the daily fine... and did they run into trouble with people resisting, or did the local police actually follow the court's orders?

It all depends on the total acreage and what that land is zoned for. If this ends up in front of a judge, the compensation is going to be determined by an expert witness's report, specifically looking at compensation for partial takings.

You aren't going to be paying a "daily rate." It’ll be one lump sum. It all boils down to the price per square foot based on the land's usage and exactly how much of the property you're occupying.

The courts move relatively fast, and the police don't have anything to do with these specific calculations.

Hello, I am looking for some guidance
Here is the situation: a licensed firm contracted by the US Army Corps of Engineers has been using a private parcel of land for several years to access a canal they are maintaining.
If they haven't requested formal permission, I assume I am entitled to compensation. On what legal grounds can I pursue this?
Furthermore, they are insisting that because they need a specific strip of land right along the ditch, I have to allow them access without any payment, regardless of the fact that it is private property. Is that actually true?
Am I able to claim compensation retroactively for the past few years?