So that means it's not an ergative verb then.
You seem to be confusing ergative constructions with passive constructions, HeartShape. They're different:
(1a) Harry broke the vase.
(1b) The vase was broken (by Harry).
(2) The vase broke.
Sentence (1a) is in the active voice, sentence (1b) is in the passive voice, and sentence (2) is an ergative construction. In both (1b) and (2), the direct object of the active-voice sentence is the subject of the sentence. However, if you look really closely at (1b), you will see two features that (2) lacks. First, there is an extra word in the verb group: "was." Second, the past participle is used: "broken."
In any passive construction, there will be those two features: a passive auxiliary (which is traditionally a form of the verb "be" -- some people would include "get") and the past-participle form of the verb. In many cases, as with "want," the past participle ("wanted") and the past tense ("wanted") are the same. But, with other verbs, such as "break," they are not the same: "broke" (past tense); "broken" (past participle).
Passive-voice constructions are often analyzed as transformations of the corresponding active-voice constructions. According to this way of looking at things, (1b) may be said to
derive from (1a). But even if one wishes to pretend that there is no syntactic relationship between the two, any native speaker can grasp the fact that (1b), even without the agent "by"-phrase, expresses that the vase has been acted upon.
The ergative construction ("The vase broke") does not have that meaning. While one can reason things through and realize that if the vase broke something or someone must have caused it to break, the sentence itself does not express that. There is the sense that it spontaneously came apart. That is why ergative constructions are convenient when one wishes to avoid assigning or implying responsibility for an event.
Note, too, that the ergative construction does not use the past participle ("broken"), and, more importantly, does not contain the passive auxiliary (a form of "be," such as "was"). I say "more importantly" because the past participle of an ergative verb can, of course, be used in ergative constructions: "The vase has/had broken." Contrast that with the passive: "The voice has/had
BEEN broken (by someone)."
Ergative verbs are few and far between. "Want" is not an ergative verb. Your sentences aren't ergative constructions. They are passive constructions, as Piscean has been explaining to you. The fact that the thing affected by the transitive verb (the patient or theme of "wanted," as some would say) is the subject of the sentence does not mean that the verb is intransitive. All passive sentences have transitive verbs.
(3a) active: Uncle Sam wants you.
(3b) passive: You ARE wanted (by Uncle Sam).
(4) ergative: *[strike]
You want.[/strike]