Many pronouns have this kind of genitive form
Genitives in -ius exist for a fairly small number of Latin words. I'm not sure of the exact amount.
I would say that the stems that take this kind of genitive form constitute a "closed class", although there a\number of derived pronouns that inherit the inflection pattern of the base pronoun (e.g. quisque, cuiusque built on quis, cuius).
The usual pronunciation is with long -ī-, as -īus, although some forms in short -ǐus are also attested in poetry, and in eius, huius, and cuius the -i- is assumed to be a long consonant [j.j].
This genitive ending is characteristic to words declined with first/second declension endings that are used as pronouns or as quantifiers/determiners. In that sense, its usage is not arbitrary nor especially unpredictable. It could be considered irregular if you wish.
There are a few pronouns with complications in the genitive singular:
I haven't put together a complete list yet.
- eius, huius, cuius
- illīus, ipsīus, istīus
Derived from these pronouns:
- eiusdem, cuiusdam, cuiuscumque, alicuius, cuiuspiam, cuiusvis
You can see some with quantifier/determininer uses listed in Allen and Greenough 113:
- The following nine adjectives with their compounds have the Genitive Singular in -īus and the Dative in -ī in all genders.
- alius [aliud (n.)] other
- tōtus whole
- alter, -terīus the other
- nūllus no, none
- ūllus any
- neuter, -trīus neither
- sōlus alone
- ūnus one
- uter, -trīus which (of two)
b. The genitive in -īus, dative in -ī, and neuter in -d are pronominal
in origin (cf. illīus, illī, illud, and § 146).
c. The i of the genitive ending -īus, though originally long, may be
made short in verse; this occurs often in alterius and regularly in
d. Instead of alīus, alterīus is commonly used, or in the possessive
sense the adjective aliēnus, belonging to another, another's.
The etymology of Latin genitive singular forms is complicated
The etymological origins of this genitive singular ending, as well as the regular -ī genitive singular ending of the Latin second declension, are not straightforward and so appear to have been extensively discussed in linguistic literature. The only paper I have read so far (and only partially digested) is "The o-stem genitive singular: Considerations from the perspective of the Latin dialects", by Luca Rigobianco (2017, Études de linguistique latine II).
Rigobianco rejects a common hypothesis that derives cuius, huius, eius from genitive singular forms in -osio- (cognate to Sanskrit -asya-) questioning the validity of the loss of -s- in this phonetic context (10). The references mentioned in favor of the hypothesis are Leumann, 1977, p. 477 and Meiser, 1998, p. 117.
I haven't read a source yet that directly discusses the forms with vocalic/syllabic -i- such as unius; it's my assumption that they would in some way be related to cuius, huius, eius.
The origin of the final -s is another difficult point; it has been explained as an added element by analogy with genitives in /s/ (as in nouns of the third declension or archaically in the first declension).