If a fence is put up on the property line is it mine as much as theirs?
If you know who put it up, no. It belongs to the person who
built it or paid to have it built, and that person is responsible
for its care and maintenance, and replacement if he so chooses.
But, if nobody can remember who put it up or when (as in the
case perhaps of a stone or masonry fence typical in the NE of the
country where the ground is exceptionally rocky from glacial
deposits), possibly both unless one or the other owner claims it or
denies ownership, and most likely that will occur when it has to be
repaired or replaced and then it may be a question of "how much" it
sits on one or the other's property (especially in the case of a
stone or masonry fence that is much wider than a typical wood fence
although there are a few styles of wood fences that can be "more or
less" on one side or the other).
Otherwise, since most people are not willing to spend the extra
money to erect a fence with "two" good sides, most current building
codes require that when you erect a fence and there is only one
good side, that the good side must face your neighbor, not your
property. In the case of most "wood" or "stockade" fences, this
means the visible fence posts must be on your side, not the
neighbor's side. Therefore, if nobody knows who put it up and it is
that kind of fence, whichever side is the "good" side would be the
neighbor's and the other side would point to the fence "owner". But
if you know who put it up, then it belongs to whoever put it up,
even if the face of the fence technically sits over the property
line even by inches or less. That's called an "encroachment" and
why, to avoid having the neighbor demand it be moved, most fence
companies will insist on having a survey of your property in order
to plant your fence posts well enough inside your property line so
that the face of it will still be on your side of the property
line.