We study the problem of sharing the revenues from broadcasting sports leagues axiomatically. Our key axiom is anonymity, the classical impartiality axiom. Other impartiality axioms already studied in these problems are equal treatment of equals, weak equal treatment of equals and symmetry. We study the relationship between all impartiality axioms. Besides we combine anonymity with other existing axioms in the literature. Some combinations give rise to new characterizations of well-known rules. The family of generalized split rules is characterized with anonymity, additivity and null team. The concede-and-divide rule is characterized with anonymity, additivity and essential team. Others combinations characterize new rules that had not been considered before. We provide three characterizations in which three axioms are the same (anonymity, additivity, and order preservation) the fourth one is different (maximum aspirations, weak upper bound, and non-negativity). Depending on the fourth axiom we obtain three different families of rules. In all of them concede-and-divide plays a central role.