The Branches of Morpheme "Allomorphs and Zero Allomorphs"

Allomorphs

An allomorph is ‘any of the different forms of a morpheme’. (Richards, Platt & Weber) that is, when a unit of meaning varies in sound without changing meaning. The term allomorph explains the comprehension of phonological variations for specific morphemes. They occur in all types of morphemes : in lexical morphemes such as official from office, in roots as in reception from receive, in derivational morphemes as in impossible vs. incorrect and in grammatical endings, such as voiced /d/ in loved vs. unvoiced /t/ in walked.

phonological conditioning - morphological conditioning - grammatical conditioning

If these allomorphs ar e determined by a preceding phoneme, they are called phonologically conditioned allomorphs. If there is no phonemic conditioning, they are called morphologically conditioned allomorphs, i.e. a certain lexical morpheme constitutes the realisation of a certain affix.

Another conditioning is the so-called grammatical conditioning, which changes the bases and not the affixes. This is the case in plural or past tense forms knives, thieves, houses and wept, slept, where the ending conditions voiced word final consonant viz. shortening of the basis. This can be demonstrated in the English plurals and past tense morphemes :

	phonologically conditioned	morphologically conditioned
plural	[z] after voiced consonants and vowels : beds, knees [s] after voiceless consonants: tulips, parents [Iz] after sibilants (Zischlaute): horses, bushes	Umlaut: feet, geese, teeth, mice -en: oxen, children zero-allomorph: fish, deer Latin/Greek loans: fungi, antennae, phenomena, theses
past tense	[d] after voiced consonants and vowels: rubbed, judged, entered [t] after voiceless consonants: stopped, kicked, laughed [Id] after [t, d]: wanted, decided	portmanteau morpheme: took, gave zero-allomorph: put, cut

Portmanteau

For cases like took or mice linguists suggested the term portmanteau morphs, i.e. one morph realises more than one morpheme or function. In these cases took contains the meaning of ´take + the meaning of past tense´ and mice contains both the morpheme ´mouse + the plural morpheme´. This is also the case in your (cars), which has three morphemes (2nd person, plural, possession) or in Latin amo (first person, singular, present, active).

Zero-Allomorph

A further abstraction is the concept of the zero-realisation (no visible affix, but a specific meaning) in plurals such as fish and deer and past tense forms such as cut and put. 

Consisting of no phonetic form, is an allomorph of a morpheme that is otherwise realized in speech. In the phrase two sheep-∅, the plural marker is a zero morph, which is an allomorph of -s as in two cows.

References :
www.anglistik.phil.uni-erlangen.de

https://en.wikipedia.org/wiki/Zero_(linguistics)