Marks, J. 2008. Zeus in the Odyssey. Hellenic Studies Series 31. Washington, DC: Center for Hellenic Studies. http://nrs.harvard.edu/urn-3:hul.ebook:CHS_Marks.Zeus_in_the_Odyssey.2008.
After the Odyssey
μοῦνον Λαέρτην Ἁρκείσιος υἱὸν ἔτικτε,
μοῦνον δ῾ αὖτ’ Ὁδυσῆα πατὴρ τέκεν· αὐτὰρ Ὁδυσσεὺς
μοῦνον ἔμ’ ἐν μεγάροισι τεκὼν λίπεν.
For thus our line the son of Kronos made single:
Laertes was the only son Arkeisios bore,
and again Odysseus was the only son his own father bore; and again Odysseus
bore me only in his halls before he left.
Apart from the simple fact that Telemachos is an only son, this information is superfluous in the immediate context of Book 16, and seems motivated in part by the irony of having the son tell family lore to his own disguised father. But the ornate rhetoric, in particular the jingly anaphora built around moun– ‘only, single’ suggests a more significant function. That function, I shall argue, is to be found in the implications of Telemachos’ statement for the Odyssey’s relationship to non-Homeric traditions.
Odysseus after the Odyssey
εἰς ὅ κε τοὺς ἀφίκηαι, οἳ οὐκ ἴσασι θάλασσαν . . .
καὶ τότε δὴ γαίηι πήξας εὐῆρες ἐρετμόν,
ῥέξας ἱερὰ καλὰ Ποσειδάωνι ἄνακτι . . .
οἰκαδ᾿ ἀποστείχειν ἔρδειν θ᾿ ἱερὰς ἑκατόμβας
Go then, taking a well-made oar,
until you reach those who do not know the sea . . .
and then in the earth fix the well-made oar.
When you have made pleasing sacrifices to lord Poseidon . . .
return home and dedicate sacred hekatombs
to the deathless gods.
Through the appointed rituals, the hero will bring to an end his protracted conflict with his divine antagonist by entering the god’s service, in which respect Odysseus resembles such figures as Erechtheus.  The transformation of Odysseus’ relationship with Poseidon seems also a necessary precondition of Zeus’ settlement for Ithake in Book 24, since a community of islanders depends naturally on a good relationship with the sea god (as the Phaiakes illustrate in Book 13). And while the predicted journey far inland seems likely to be arduous, no hazards or intrigues are noted, and Odysseus’ safe return is guaranteed.
ἀβληχρὸς μάλα τοῖος ἐλεύσεται, ὅς κέ σε πέφνηι
γήραι ὑπὸ λιπαρῶι ἀρημένον· ἀμφὶ δὲ λαοὶ
Your own death will be [far from/away from/out of] the sea,
a very [gentle/feeble] sort it will be when it comes, which kills you
when you are worn out by sleek old age; and around you the people
will be prosperous.
The sympathy between Teiresias’ prophecy and Zeus’ settlement is evident in the stipulation that “the people will be prosperous” when Odysseus dies (cf. 24.486). Further, Teiresias’ scenario of a peaceful death, in old age, and during a time of prosperity, implies the seamless transfer of power from ruler to son, Odysseus to Telemachos, that Zeus’ settlement implies.
A similar tradition is preserved in “Apollodoros”: Odysseus, after killing the suitors,
Though it has no part in Homeric tradition, Telegonos’ story did evolve sufficiently to take a variety of forms, including references in Hesiodic epic and Attic tragedy.  Again, even if these specific accounts post-date the Odyssey, the latter at least evinces awareness of similar themes.  On the one hand, this awareness is betrayed through wholesale de-authorization, as in the case of Telemachos’ assertion and Zeus’ settlement. But the Odyssey also appears to target themes specific to antithetical versions of its hero’s story.
ἔνθ᾿ Ὀδυσῆος ἐγὼ πυθόμην· κεῖνος γὰρ ἔφασκε
ξεινίσαι ἠδὲ φιλῆσαι ἰόντ᾿ ἐς πατρίδα γαῖαν·
καί μοι κτήματ᾿ ἔδειξεν, ὅσα ξυναγείρατ᾿ Ὀδυσσεύς . . .
τὸν δ᾿ ἐς Δωδώνην φάτο βήμεναι, ὄφρα θεοῖο
ἐκ δρυὸς ὑψικόμοιο Διὸς βουλὴν ἐπακούσηι,
ὅππως νοστήσηι Ἰθάκης ἐς πίονα δῆμον,
ἤδη δὴν ἀπεών, ἢ ἀμφαδὸν ἦε κρυφηδόν.330
ὤμοσε δὲ πρὸς ἔμ᾿ αὐτόν, ἀποσπένδων ἐνὶ οἴκωι,
νῆα κατειρύσθαι καὶ ἐπαρτέας ἔμμεν ἑταίρους,
οἳ δή μιν πέμψουσι φίλην ἐς πατρίδα γαῖαν.
There the king of the Thesprotians, Pheidon, entertained me . . .
there I myself heard about Odysseus; for he kept saying
that he had hosted Odysseus and treated him kindly as he was going to his paternal land;
and he showed me possessions that Odysseus had gathered . . .
and he said that he had gone to Dodona, so that from the god’s
lofty-leafed oak he might learn the plan of Zeus (Dios boulē),
how he would return home to the rich people of Ithake,
having already been away for a long time, either openly or in secret. 
And he [Pheidon] swore to me myself as he was pouring libations in his house,
that a ship had been drawn down [to the sea] and comrades were ready,
who will send him to his own paternal land.
Such a mission would be plausible to Homeric audiences since historical Dodona was the site of a well-known oracle of Zeus. The question that “Odysseus” is to ask Zeus’ tree-oracle at Dodona, regarding how he should arrive on Ithake, is reproduced in Teiresias’ prophecy, which also admits the possibility of Odysseus’ “open” return (again, ἠὲ δόλωι ἢ ἀμφαδὸν ὀξέι χαλκῶι, 11.120; cf. 14.330=19.299). Likewise, Nestor suggests to Telemachos that his father may return and exact tisis from the suitors “either alone or all the Achaians as well” (ἢ ὅ γε μοῦνος ἐὼν ἢ καὶ σύμπαντες Ἀχαοιοί, 3.217).  What “Odysseus” is apparently pondering in these lying tales is the possibility of returning at the head of an army, for Pheidon has offered ships and men to aid in his repatriation. He is however leaving it to Zeus to decide the terms of his return, which is to say that control over the course of this ersatz Odyssey rests, as over that of the main narrative, with Zeus.
A fragment from the Aristotelian Constitution of the Ithakans preserves a related account:
As in the Telegony, Odysseus departs, marries into the royal family, and fathers epigonoi; here, however, he does not return.  Most importantly, the present passages make explicit that Odysseus departs Ithake as a direct consequence of the Mnesterophonia.
The Odyssey and west Greek epichoric tradition
Δωδώνης μεδέων δυσχειμέρου, ἀμφὶ δὲ Σελλοί
σοὶ ναίουσ᾿ ὑποφῆται ἀνιπτόποδες χαμαιεῦναι
Zeus lord, Dodonan, Pelasgian, dwelling far off,
ruling Dodona where the winters are harsh; and around the Selloi
dwell, your intepreters, their feet unwashed, sleeping on the ground
The reference to “interpreters” (ὑποφῆται) alludes to the status of Zeus’ Dodonan cult as an oracle. That the oracle is assumed to be known to audiences of the Iliad is implicit in the fact that Achilleus, though his homeland is on the opposite side of the mainland, invokes Zeus by a west-Greek cult title, and is aware of peculiar practices of the priests of this cult.  The distinctive priesthood in the Iliad complements, rather than conflicts with, the prophetic trees referred to in the Odyssey, since both seem to have been aspects of the “real” cult of Zeus at Dodona. 
Aitolia and Elis
West Greek epichoric tradition