What exactly are the Indo-European predicative mine/yours/ours/his/hers/its/theirs forms, in terms of word class and inflection? Would they be considered the genitive (or even the dative) case of personal pronouns, a nominalized (or genitive) form of possessive adjectives, or something distinct?
Looking at German, the forms for the genitive, dative, possessive adjective, and predicative possessive are clearly distinct (e.g. genitive 'meiner', possessive adjective 'mein', dative 'meinem', and predicative 'meins'), though the genitive of personal pronouns is rare in modern German. There is some resemblance between the genitive case of possessive adjectives and the predicative forms; I kind of wonder if there might have been a progression of "It is [one] of my things" to "It is mine", but that's kind of tenuous.
In English they kind of look like the possessive adjective + -'s, but that's also pretty tenuous. Looking over Beowulf I kind of got the impression that in Old English the dative of possession was used for predicative possession.
As I understand it, the genitive of the personal pronoun or dative of possession would have been used predicatively in Latin, and I haven't heard of a dedicated predicative form.