Q:

What are some uses of the Magnificat, Benedictus and Nunc Dimittis in the Eastern Rites? 

I'm referring to Catholic Eastern rites, and possibly to Orthodox ones as well.  I'd like to know their place in the Divine Office.  Feel free to point the use in any rite (e.g., Byzantine, or other ones). 
Information I seek is, for example, that in the X rite they are chanted at Y time of the day, together or not, maybe with some psalms in between, at the start, in the middle or at the end of the Office, before or after readings of the Scriptures... things like this. 
But even very basic information is appreciated (e.g., in rite X the Magnificat is chanted in the office Y). 

A:

For the Eastern Orthodox Church:

Magnificat: Sung at daily Matins, after the Psalter readings and Psalm 50 (LXX)
Benedictus: I don't believe is sung regularly at any service.   It is, however, the Gospel reading for Matins and the Divine Liturgy on the Feast Day of the Nativity of John the Baptist (June 24)
Nunc Dimittis: Read during each daily Vespers, near the end of the service. 

I believe this is the typical usage for most Typicons (e.g. Russian, Greek, etc.)