If one says: I am going to run. What is the "am going to run" verb called? Compound? Auxialiary plus infinitive? What? Thanks loads.
BE going + to is generally considered to be an auxiliary verb. Be going is followed by the to-infinitive of the full verb.
NOT A TEACHER
(1) Great question.
(2) According to my books, you have hit the nail on the head.
(3) Here is what one book says about "I have to go." The infinitive "to go" combines with the auxiliary verb "have" to form a verb. It = I must go. (Source: A Grammar of Present-Day Grammar by Pence & Emery, 1947 (first copyrighted).)
(4) Here is what another book says about "The sun is going to rise." Again, the infinitive "to rise" combines with the auxiliary "is going." This book has a special term for an infinitive that is used in this way: complementary infinitive.
(a) And as you have probably already guessed, that is just another way of saying: The sun will rise. (Source: Descriptive English Grammar by House and Harman, 1931 (first copyrighted).)