The Syro-Malabar and Syro-Malankara Catholic churches in India also use variants of the Antiochene Rite. The Syro-Malabars are actually the second-largest Eastern Catholic church, after the Ukrainians.
“The Maronite liturgy is the Antiochene Rite (Liturgy of St. James) with some Latinizations.”
Here’s a link to an explanation of the Maronite Liturgy from a Maronite source.
http://www.stgeorgesa.org/explanation_of_the_maronite_divi.htm
I have been to Maronite Liturgies. I must say they seem to bear little resemblance to the Liturgy of St. James, though I don;t doubt that the modern “experimental” Maronite liturgy is based on it. Here’s a link
http://www.ccel.org/ccel/schaff/anf07.xii.ii.html
The Liturgy of St. James is indeed Antiochene and it is very, very long. In its ancient form it is still said here and there and as such is the most ancient continually used Liturgy of The Church.