What I call a contextualizer fits this description more or less. But I break company with POINT OF DEPARTURE over the issue of discontinuity. I think it is useful to talk about constituents in front of the nuclear clause that relate what follows to the context. Marking discontinuity is a different issue from contextualizing and I don't consider it useful to bundle the two concepts.Definition:
The term POINT OF DEPARTURE designates an element that is placed at the beginning of a clause or sentence with a dual function.
1. It establishes a starting point for the communication; and
2. It “cohesively anchors the subsequent clause(s) to something which is already in the context (i.e. to something accessible in the hearer’s mental representation).” (Dooley & Levinsohn 2001:68)
Mark 1:10 is an example ἀναβαίνων ἐκ τοῦ ὕδατος ties the vision εἶδεν σχιζομένους τοὺς οὐρανοὺς to the baptism.Mark 1:8 ἐγὼ ἐβάπτισα ὑμᾶς ὕδατι, αὐτὸς δὲ βαπτίσει ὑμᾶς ἐν πνεύματι ἁγίῳ. 9 Καὶ ἐγένετο ἐν ἐκείναις ταῖς ἡμέραις ἦλθεν Ἰησοῦς ἀπὸ Ναζαρὲτ τῆς Γαλιλαίας καὶ ἐβαπτίσθη εἰς τὸν Ἰορδάνην ὑπὸ Ἰωάννου. 10 καὶ εὐθὺς ἀναβαίνων ἐκ τοῦ ὕδατος εἶδεν σχιζομένους τοὺς οὐρανοὺς καὶ τὸ πνεῦμα ὡς περιστερὰν καταβαῖνον εἰς αὐτόν· 11 καὶ φωνὴ ἐγένετο ἐκ τῶν οὐρανῶν· σὺ εἶ ὁ υἱός μου ὁ ἀγαπητός, ἐν σοὶ εὐδόκησα. 12 Καὶ εὐθὺς τὸ πνεῦμα αὐτὸν ἐκβάλλει εἰς τὴν ἔρημον. 13 καὶ ἦν ἐν τῇ ἐρήμῳ τεσσεράκοντα ἡμέρας πειραζόμενος ὑπὸ τοῦ σατανᾶ, καὶ ἦν μετὰ τῶν θηρίων, καὶ οἱ ἄγγελοι διηκόνουν αὐτῷ. 14 Μετὰ δὲ τὸ παραδοθῆναι τὸν Ἰωάννην ἦλθεν ὁ Ἰησοῦς εἰς τὴν Γαλιλαίαν κηρύσσων τὸ εὐαγγέλιον τοῦ θεοῦ
This issue came up while I was exploring the question of discourse prominence and participles. In Mark 1:10 ἀναβαίνων ἐκ τοῦ ὕδατος is "background" for εἶδεν σχιζομένους … καταβαῖνον, where the participles in the vision form a linear time sequence. The vision is an embedded narrative. Not sure if the voice φωνὴ ἐγένετο in verse 11 is part of the embedded vision narrative or on the same level with εἶδεν. I lean toward the later analysis. The vision and the voice are very important to the narrative.
 I don't think my definition of contextualizers is identical to Randall Buth's. Yesterday I read his paper on the verbless clause in Hebrew. At times he seems to be talking about discontinuity and sometimes entire clauses function as contextualizers. I have no problem with entire clauses but I think Randall is doing something subtle that I haven't as yet figured out. See: Buth, Randall. Word order in the verbless clause: A generative-functional approach. In The Verbless Clause in Biblical Hebrew, edited by Cynthia L. Miller, 79-108. Winona Lake IN: Eisenbrauns. http://www.biblicallanguagecenter.com/w ... h-1999.pdf