What pronoun should be used in the sentence: "All of the players signed (his or her, their) jerseys"?

The most appropriate pronoun in this context is "their." In the sentence "All of the players signed (his or her, their) jerseys," the use of "their" serves as a plural pronoun that collectively refers to all players.

When using "all," the subject is understood to be plural, and thus "their" correctly agrees in number. It reflects a common practice in English to use "they/them" as singular gender-neutral pronouns as well, which fits modern usage for inclusivity. Moreover, "their" naturally indicates possession, aligning with the context of jerseys being signed by each player.

In contrast, "his or her" is a singular pronoun phrase, which does not match the plural nature of "players," and "its" is a pronoun used for singular neuter nouns and does not apply to people. "Them" is an object pronoun and cannot function as a possessive pronoun, making "their" the clear choice in this sentence.