Stephen Jones wrote: Some time ago Metal56 linked to an article by a teacher at the British Council in Estonia, who had basically published online a rehash of Lewis combined with attacks on Swann and some added inaccuracies of the author's own devising. I attacked the paper as being 'hopelessly amateurish' and drew the wrath of Larry, but if the guy had the least formal training he would never had claimed that the 'to' in I want to see you went with 'want' and not the following verb phrase. He was attempting to refute the idea that there was something wrong with the split infinitive, but in doing so, made an ass of himself. Linguists have assigned various categories to the 'to', including that of a defective auxiliary verb, but there is no doubt that it goes at the beginning of the Verb Phrase, and the best description is probably that of a marker (the CGEL suggests a subordinator) coming before the head of the VP 'see you'.
In spoken language, you can say
Mother: No, Sally, you cannot stick your fork in the electrical outlet.
Sally: But I want to.
"I want to" used in this way is pretty common (at least in some varieties of English). If the "to" did not go with the "want" then it would be correct to say "But I want", which is a common error made by some non-native speakers.
In fact, this is an example of exactly the kind of thing taught in at least some university teacher training programmes.