An accredited Texas-bred Thoroughbred or Arabian horse described by Section 2021.003(50)(C) is eligible for one-half of the incentives awarded under Sections 2028.103(a) and 2028.105(d)(2). The appropriate state horse breed registry shall retain the remaining portion for general distribution at the same meeting in accordance with Sections 2028.103(a) and 2028.105(d).