Is them a nominative objective or possessive?

The pronoun 'them' is the objective form of the pronoun 'they'.

The pronouns 'they' and 'them' are the third person, plural, personal pronouns.

The pronoun 'them' functions as the object of a verb or a preposition.

Example: The Walters came to visit and theybrought the baby with them. (object of the preposition 'with')