The law on the sharing of costs of dividing fences, including boundary walls is dealt with under the Dividing Fences Act:
Essentially each party is normally obliged to share the reasonable cost of repair or replacement of a boundary fence, provided the party replacing/reparing the dividing fence follows certain procedures.
However, if each of you have built your own fences alongside one another, so they effectively serve the same function as a dividing fence, then you will each be liable for your own fence until such time as one or the other of you removes such a fence.
Regardless of the above, the issue that is of potentially greatest concern is that if you neighbour or their predecessor in title build a wall which encroaches on your land, they may be entitled to claim any such land walled off by this encroachment due to the principle of adverse possession. If the strip of land is significant in size it may be that this is an issue you should immediately seek thorough legal advice about, as entering into a fence dispute in such circumstances may just tip your neighbour off as to their entitlement to claim the strip of land, whereas in some circumstances, if appropriate action is taken it may be possible to re-secure your title to the strip provided you act before your neighbour is alerted to their potential claim. You can read about the issue here:
If you need to engage a lawyer to consider your situation in more detail and you need assistance locating a suitable lawyer, contact the Law Society of WA:
I trust the above assists.
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