I want to go home.
Here the word to belongs to what part of speech?
I want to go home.
Here the word to belongs to what part of speech?
I want to go home.
I'd say that infinitival "to" belongs to the word category (POS) 'subordinator', and its function is that of 'marker', a meaningless element that simply introduces the VP.
It functions in much the same way as the indisputable subordinators "that", as in I know that she lent him the money" and "whether", as in I'm unsure whether it will rain.
Note that infinitival "to" derives historically from the preposition "to" (notice the strong similarity between I went to the doctor and I went to see the doctor) but long ago lost its prepositional properties.
It belongs to no morphological category, that's why it is named a particle.
The usual definition of particle is that it is a word that does not clearly belong to any other word class - though the expression is also used for the type of adverb particle found in phrasal and phrasal prepositional verbs. English has two such particles, the infinitive particle TO and the negative particle NOT. (source)
It is not a preposition, neither is it a part of the verb, as Grammarphobia shows:
The infinitive is the uninflected or basic form of a verb, and “to” is not part of it. When “to” appears with an infinitive, it is generally referred to as an “infinitive marker” or “infinitive particle”; it is not part of the verb and is not always used.
The same site cites reputable sources in support of this:
Fowler’s Modern English Usage (rev. 3rd ed.), describes two uses of the infinitive: (a) “the to-infinitive,” in which “to” is described as a “particle,” and (b) “the bare or simple or plain infinitive.”
The Cambridge Grammar of the English Language explains that:
The traditional practice for citation of verbs is to cite them with the infinitival marker to, as in ‘to be,’ ‘to take,’ and so on. That is an unsatisfactory convention, because the to is not part of the verb itself.
The word “to” here “is not a (morphological) prefix but a quite separate (syntactic) word,” Pullum and Huddleston say, adding:
This is evident from the fact that it can stand alone in elliptical constructions (as in I haven’t read it yet, but I hope to shortly), need not be repeated in coordination (as seen in I want to go out and get some exercise), and can be separated from the verb by an adverb, as seen in the so-called ‘split infinitive construction,’ I’m trying to gradually improve my game.
The site cites similar explanations from other established dictionaries, I will not quote them all here. But I cannot omit the OED entry they quote, as it shows the morphological shift of this particle:
Quote from the OED:
The infinitive with to may be dependent on an adj., a n., or a vb., or it may stand independently. To an adj. it stands in adverbial relation: ready to fight = ready for fighting; to a n. it stands in adjectival or sometimes adverbial relation: a day to remember = a memorable day; to a vb. it may stand in an adverbial or substantival relation: to proceed to work = to proceed to working; to like to work = to like working.”
When this preposition was first used in English as an infinitive marker (tó in Old English), it did have a prepositional flavor. “I prepared to eat” sounded to the medieval ear something like “I prepared for eating”; “he fails to think” sounded something like “he fails in thinking”; “we strive to please” sounded something like “we strive toward pleasing.” As the OED says,
it expressed motion, direction, inclination, purpose, etc., toward the act or condition expressed by the infinitive; as in ‘he came to help (i.e. to the help of) his friends,’ … ‘he prepared to depart (i.e. for departure).’
There once was a sense of motion, of moving toward accomplishing something (represented by the infinitive), if that makes any sense. But as the OED says:
in process of time this obvious sense of the prep. became weakened and generalized, so that tó became at last the ordinary link expressing any prepositional relation in which an infinitive stands to a preceding verb, adjective, or substantive. [Here the italicized tó represents the Old English word.]
PS: The research I have just done for this answer makes me wonder: then why on earth is the to-infinitive also called full infinitive? But that's maybe worth asking in a different post.
It depends on who you ask. Within the confines of traditional parts of speech, the present-day to in the infinitive may be a preposition or it may a particle.
Even in the 19th century, grammarians were wary of assigning the to-infinitive to a single part of speech. For example, if you look up preposition in George Pliny Brown's 1899 book Advanced Pages of Elements of English Grammar, you would find nothing resembling the to-infinitive. Instead, "The Infinitive" would be listed under the hedging header "Words Sometimes Called Parts of Speech" with "The Participle," "The Article," and "The Gerund." Brown describes the infinitive as having some functions of both a verb (in how it can be modified) and a noun phrase (in how it can be the subject of a sentence). In other words, Brown is illustrating the traditional grammarian's difficulty to reconcile the structured parts of speech with forms that don't fit well in the existing theory. The to-infinitive, let alone to itself, is right at that fault line.
The Oxford English Dictionary reflects the difficulty of defining to before an infinitive under "to, prep., conj., and adv.," definition B. The full explanation is too long to quote in full, but I want to highlight two elements of that explanation:
The to preceding the infinitive comes from Old English, where it would have been considered a preposition (tó [see Bossworth Toller]). An example of the preposition-based usage with a verb of motion (come to) is under I.1.a.(a) from Bede: "Monige cwomon to bicgenne þa ðing" [Many came to buy the thing]). In that kind of usage, even today, the OED would consider to a preposition: "But after an intransitive verb, or the passive voice, to is still the preposition."
In other uses of the to-infinitive not evident in Old English, e.g., using the infinitive as a subject, to is considered to have "lost all its meaning, and become a mere 'sign' or prefix of the infinitive." Though the OED wants to call this to a prefix, a morphological attachment to the word, that description is quite close to the definition of a particle, a word that doesn't fit conveniently into other parts of speech or classes of words (Wikipedia).
It's worth noting that the OED is not an authority on grammar, and its primary purpose isn't creating rigorous classifications of language use. Nonetheless, it represents what later systems will generally show: while the infinitive to once functioned as a preposition, in modern English that language is no longer sufficient to describe what to is doing in many infinitive uses. Hence it is often called a particle.
'To' in 'to kick' is, according to Wikipedia, an infinitival particle. The infinitive 'to kick' without 'to' so just 'kick' is called the bare infinitive, whilst 'to kick' is called the full infinitive.