See A.D.'s reposte in the above.
I don't know how much light the following sheds on the matter, but it speaks to the oral tradition of the Homeric poems and the possibilities of authorship:
"The War at Troy (What Homer Didn't Tell)"; Quintus of Smyrna, Translated by Frederick M. Combellack
1968, Univ. of Oklahoma Press.
"Quintus' epic, written probably in the third century A.D., is the only extant literary work from antiquity that gives a connected account of the events of the Trojan War, which took place between the death of Hector and the departure of the Greeks. It tells what happened to Achilles and to Troy, and many other things besides - among them the fatal enterprises of the Queen of the Amazons and the King of Ethopia, the funeral games held in Achilles honor, the victory of Odysseus in his contest with Ajax for Achilles splendid armor, the death of Paris, the strategy of the wooden horse, and the capture and sack of Troy." (From the fly leaf of the book.)
I think that most believe that the above is in the Iliad and the Odyessy.
What I am trying to get at is that there was an oral tradition in antiquity, and simply because Homer is accredited with the poems, does not prove that 'he' wrote them.