2 landowners, 1 fence

I'm sure it probably varies from state to state, but the law in New York State is that the animal owner is responsible for fencing their animals in. Anything other than that is a gentleman's agreement between neighboring landowners.

Some folks informally use the right hand rule but unless written in a statute, that's not legally binding.

Some states also don't require a landowner who doesn't keep livestock on their property to maintain the fence, and all the burden is on the other landowner if they are the only ones keeping livestock in.

You will have to look the laws up for your state... Potentially county if there is anywhere that a county has more specific laws?

Kansas is a open range state,meaning livestock always have the right of way and when it comes to fences basically around here if you have the livestock then the fence is 100% your responsibility, now if there's livestock on both sides it's usually a gentlemen agreement that they will split the cost of the fence.  I have several pastures that border neighbors with cattle and occasionally one will offer to pay for supplies, however my whole life I've just got what I needed and built or fixed the fence, it's just a lot easier than dealing with some cry baby neighbor that thinks this is right or that costs to much, etc, and when I'm done I don't give a crap what they think if they don't like it they could have got off there backside and did it themselves, however I've never heard a peep from any of them.  Free 99 is hard to complain about.

Funny story, if you ever go south of Ceda Bluff Res. about 3 1/2 miles south of the dam you'll see a big Jayhawk setting about 1/4 west of the highway.  Years ago a now deceased friend of mine had a section of grass and the land that surrounded him was donated to K-State by his aunt when she passed.  Anyways his property had 1 mile of shared fence at the south end with K-State and they sent letters out to all the land owners that they adjoined wanting them to pay for half the materials and they would pay all labor.  My friend and I talked about it and both agreed that was a hell of a deal and for him it was the last mile of fence out of 4 that he hadn't already replaced in the last 4 years out of his own pocket.  So he did nothing planning on agreeing to their terms.  Well later that winter my friend after seeing the big steel Indian silhouettes west of Ness City decided he wanted to do something like that in his pasture.  I told him well K-State owns the ground south and east of you and a K-State booster owns the ground north of you, so you better put a Jayhawk to represent the KU fans because your surrounded by K-State.  Well he loved that idea so we made a 10ft tall 4 ft wide Jayhawk out of 3/16 steel sheet, mounted it on 3 case rear wheel weights and set it up in the pasture and ran power for a night spotlight.  Sure looked good, pretty much like it was walking through his pasture.  Well wouldn't you know it but about a month later K-State sent a letter to all their neighbors that they would be paying for 100% of all fence costs as they didn't want to upset any neighbors that weren't interested in a new fence.  Till he died we would laugh about the coincidence of that letter and our winter project.  

Oh and he like me could care less whether your a K-State fan or KU.  Although over the years the Jayhawk as taken some lead and was once painted like a crow, although some local KU fans quickly repainted it and as far as I know it still stands there today, however I haven't been by it in 6-7 years.

We immediately built a new fence (insurance agent's recommendation) everywhere the neighbor had built fence and maintained it until we no longer used the pasture.

There are exceptions to this; I rented a farm 30 yrs ago that the building sites had mine in left 1/2 and the other on other end of section. You cared for fence closest to your bldgs. This was even written in my lease. They were so legal on it from early 1900's that agreement was recorded at county courthouse recorders office.