(a) Concurrently with the imposition of county taxes by the commissioners courts, the board shall impose a tax for the authority on all taxable property in the authority that is subject to taxation. The board shall immediately certify the tax rate to the assessor-collector of each county located wholly or partly inside the authority.
(b) The tax assessor-collector of each county located wholly or partly inside the authority shall act as the tax assessor-collector for the authority for property in the authority located in that county.

(c) The fee of each county tax assessor-collector for assessing and collecting the authority’s taxes may not exceed one percent of the taxes collected, to be paid over and disbursed in each county in the same manner as other fees of office.