Upon payment of fees provided in RCW 36.18.010, and if the surface owner files the claim of abandonment and extinguishment, together with a copy of the notice and the affidavit of publication, as required in RCW 78.22.050, in the county auditor's office for the county where such interest is located then the mineral interest shall be conclusively presumed to be extinguished.

If a statement of claim of mineral interest is filed by the current mineral interest owner within the sixty-day period provided in RCW 78.22.050, together with payment of fees provided in RCW 36.18.010, the county auditor shall record, index, and make special notation in the index of the filing.