This (from :http://www.lectlaw.com/files/lat05.htm)

If someone erects a fence on a boundary line, the fence remains that
person's unless, or until, the neighbor uses the fence--which in most
states means until the neighbor actually encloses her property.

If someone encloses his property, using an already existing fence on
any side, most state fence laws require that he pay the other owner for
the value of the fence. In other words, he must actually buy a share of
the fence. Then he becomes a co-owner of the boundary fence. California
describes this as a refund to the other owner of a just proportion of
the value of the fence at that time.(16) Many states set the required
payment at one half of the value of the existing fence to the other
landowner.