No – There is no general rule about whether you own the fence on the left or the fence on the right of your property. The truth of the matter is this: it is the vendor who breaks up the land into smaller parcels before selling each parcel individually who assigns responsibility for the boundaries of the new land parcels that he creates. If he remembers to do so, then he will identify in the conveyance deed (or the transfer deed) the boundaries for which the purchaser is responsible.
Boundary Problems website here
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