Upon the adoption of an order of annexation, the petitioning district shall be deemed dissolved, except that if there is any outstanding indebtedness of the petitioning district at the time of the dissolution thereof, the board of the annexing district shall furnish annually to the board of supervisors of the county in which the petitioning district is situated, or, if such district is situated in more than one county, then to the board of supervisors of each county in which any portion of the district is situated, an estimate in writing of the amount needed (computed as provided in Chapter 1 (commencing with Section 75350) of Part 8 of this division) for the payment of such outstanding indebtedness of the petitioning district in like manner as though the district had not been dissolved.