You are responsible for half of the partition fence of the border. It's BS, I know! Generally, most people go by the right hand rule, however, that isnt really set in stone. You can come to an agreement with that particular landowner with something different. Now, you said he wants to replace the existing fence. If it can hold cattle still, I wouldnt piss with it. It's just your job to maintain it so the cattle dont get on your side. If his cattle get onto your property because you didnt maintain your half and cause damage, you cant do crap about it. I HATE CATTLE. Some of these cattle farmers (like my neighbor) just want new fence all the time. But, they also get to claim it on their income taxes. We don't.