The history of the genitive case in English as a grammaticalisation of the determinative function.
In Old English (= OE), the genitive case was used for case marking of a noun/phrase as, among other functions, modifier of a noun (adnominal genitive), with various types of “genitive” relationship between the head and the modifier (as in (1), (2), (3)) or as a verbal complement (adverbal genitive, as in (4)):
(1) þæs hælendes moder (CH15, 15)
“the Saviour’s mother” (relation = kinship)
(2) We wyllað to trymminge eowres geleafan. eow gereccan … (CH2, 3)
“We will, for strengthening of your faith, tell you …” (relation = objective)
(3) & gif he forlyst an ðæra sceapa. (CH24, 8)
“And if he loses oneof those sheep …” (relation = partitive)
(4) On ðisum life we behofiað. hlafes & lare. & huselganges; (CH19, 195)
“In this life we needbread, teaching, and communion”
After the end of the OE period, all the adverbal genitive disappeared, and also some subtypes of adnominal genitive, such as partitive genitive or objective genitive. The demise of these (sub)types of genitive has been explained satisfactorily, neither has been the fact that in OE the genitive case could be used both in adnominal and adverbal functions.
I compare the history of the genitive in English to that of the auxiliary verbs, both as cases of category-split. It has been argued that in OE the two categories “lexical verbs” and “auxiliary verbs” were not distinct, which explains the reason why the same verbs could be used both in lexical verb function and auxiliary-like function (cf. OE cunnan “to know” and “can”). Later in the history, the two categories became more distinct, which resulted in the inability for auxiliary verbs to function as lexical verbs (e.g. not taking a nominal complement).
A similar category-split happened within a noun phrase. Assuming the analysis of the genitive/possessive morpheme in Present Day English (= PDE) as determiner, in PDE there is a clear-cut distinction between the determiner class and the nominal class. Therefore prototypical members of the determiner class cannot occur in the syntactic context for a member of the nominal class (e.g. as a verbal complement), or vice verse. In OE, however, the distinction between these two categories was not so distinct. In other words, a noun (phrase) inflected for the genitive case in OE essentially belongs to the nominal class, together with noun (phrases) inflected for the other cases (nominative, accusative, dative). Certain types of genitive noun phrases, those in adnominal functions, especially when they designate an animate, definite entity (as in the example (1) above) could also function in the determinative function (and they almost always occurred before the head noun). This determinative function of the genitive noun phrase was grammaticalised, in accordance with the emergence of the structural position of a determiner within a noun phrase, and became its sole function, to the exclusion of all non-determinative functions of the case.