(A)

1. (1) By the twenty-fifth day of July of each year, the tax commissioner shall estimate and certify the following for each county to its county auditor:

   1. (a) Its guaranteed share of the ensuing year's fund balance;
   2. (b) Its share of the excess of the ensuing year's fund balance;
   3. (c) Its total entitlement.
2. (2) In December and in June following such estimations and certifications, the commissioner shall revise such estimates and certify such revised estimates to the respective county auditors.

(B) By the tenth day of each month the commissioner shall distribute the amount credited to the public library fund in the current month under section 131.51 of the Revised Code. The distributions shall be made as follows:

1. (1) During the first six months of each year, each county shall be paid a percentage of the balance that is the same per cent that the revised estimate of the county's total entitlement certified in December under division (A)(2) of this section is of the sum of such revised estimates of the total entitlements for all counties.
2. (2) During the last six months, each county shall be paid a percentage of the balance that is the same per cent that the revised estimate of the county's total entitlement certified in June under division (A)(2) of this section is of the sum of such revised estimates of the total entitlements for all counties.

3. (3) During each of the first six months of each year, the payments made to each county shall be adjusted as follows:

   1. (a) If the county received an overpayment during the preceding distribution year, reduce the sum of the payments by the amount of such overpayment. The reduction shall be apportioned over the six months.
   2. (b) If the county received an underpayment during the preceding distribution year, increase the sum of the payments by the amount of such underpayment. The increase shall be apportioned over the six months.

(C) By the twentieth day of December of each year, the tax commissioner shall determine and certify to the auditor of each county each of the following with respect to the current distribution year:

1. (1) The year's fund balance;
2. (2) Each county's guaranteed share;
3. (3) Each county's share of the excess;
4. (4) Each county's total entitlement;
5. (5) Each county's net distribution;
6. (6) The amount by which each county's net distribution exceeded or was less than its total entitlement, which amount shall constitute the county's overpayment or underpayment for purposes of division (B)(3) of this section in the ensuing distribution year.