If a homeowner builds a fence on the property line does that fence then become the shared property ?

Normally you would not put a fence directly on the property line. In fact, most city ordinances forbid it. It has to be on one side or the other.

Normally you would not put it directly on the line because there has to be ample room to be able to maintain the other side of the fence without walking on the neighbor's property. Also, the fence posts have to be facing you and not your neighbor out of courtesy.

Did you agree with the neighbor on placing the fence right on the property line? If so, than you can do whatever you want with your "side" of the fence. I'm surprised the code enforcer would permit this project without your approval.

property fence will usually have a guideline code thru your city or county. generally the fence has to be several inches behind the actual property line, and is the responsibility of the property owner to maintain and upkeep the fence, when the new owner bought the house he/she bought the fence to. Now some townships may have their own clause in zoning when it comes to property lines

Depends on which state you're in. In Kentucky, a fence has to be built at least 6" onto your property. If it's any less, the neighbor can have you remove it and moved to where it should be or they will own that 6" of your property.

So much for the common wealth state eh?

Normally any fence built between two seperate properties has to be paid for jointly by both property owners and agreed on as to what it is to be built out of.

I guess you would have to check for rules in your area as far as where it is to be built according to codes etc.

It is a joint-owned fence. You need their permission (or they need yours) to take it down. Full ownership is if you (or they) put one up on their side of that fence or a new fence where one wasn't, 6 inches on their side of the line...