As is well known, English has two genitive or possessive constructions, the ‘proposed’ and the ‘postposed’, exemplified in (1).
In each case we have an NP, with a head N (book, office, dog, house, plants) modified by a possessive expression (John's, a man's, mine, etc.). This expression is itself an NP in the genitive Case, and I shall refer to it as the ‘genitive phrase’. By contrast with other familiar languages more highly inflected than English, genitive Case is hot marked by an inflection on the head of a genitive phrase, but by the clitic ’s, which is attached right at the end of the phrase. The exception is where the genitive phrase is not a full NP but a personal pronoun, in which case we get an inflected form (irregular in pattern) as in these other languages: I - my/mine, he - his, etc. These possessive forms of pronouns have almost identical distribution to that of full NPs in the genitive (there are some differences which I shall point to below), and so it seems clear that they are genitives, despite the morphological difference; personal pronouns are highly irregular morphologically anyway, and not only in English. This is assumed in all recent work I know of, and I shall take it to be uncontroversial.