apportion

transitive verb | \ ə-ˈpȯr-shən \ | ap·por·tion

1. a : to divide (an amount due in tax or other liability) among the parties responsible for respective shares of the payment — compare contribution

   b : to assign (a portion of the consideration agreed to in a contract) as payment for the other party's partial performance

   c : to distribute (corporate dividends) based on some proportion

   d : to assign (legislative representatives and taxes) among the states as provided by law