Early in the Odyssey we see Telemakhos as a rash, untrained boy. He clearly is not Odysseus' equal as a host, leader, or fighter. However, as the book goes on we see Telemakhos become more and more like his father, in every respect as he is taught and guided by some of the best examples he could have, Athena, Nestor, and Menelaos. By the end of the fight with the suitors we see him in a new light, he has matured from the youth we saw to the man he should be.
Telemakhos tries to emulate his father to the best of his ability, striving to be a good host as he did with Mentor. He succeeds more than we expect him to, for though he has had very bad examples to look up to for the last four years, he has heard about and dreamed of his father constantly. It is as if Odysseus did raise his son in some ways, through dreams and stories, perhaps doing an even better job that way than he could have in person. In dreams and stories, more often than not, the one who is fantasized about can do no wrong and is the perfect icon to look up to. In person you can see how flawed the person really is, lowering your opinion and ideals.
Telemakhos is forced to mature at an astounding rate, traveling far from home and risking his life to learn of his father. His trip teaches him more than he could ever have learned staying at home with the suitors. From Nestor and Menelaos he learns both courage and bravery, how to be both a man and a host. His understanding of how the world works evolves from abstract ideas to pure ideals under their guidance. He learns that he must fight against what the suitors represent, to take his place and not let them take it. Nestor and Menelaos guide Telemakhos, with Athena's help, toward manhood, a destination he is long overdue for.
When Odysseus finally does reach home Telemakhos is the first person he reveals himself to. Their reunion is a very happy one, joy leading to tears. Odysseus immediately treats him like an inferior however, telling Telemakhos his plans and expecting him to carry them out. This is a role that, perhaps, Telemakhos still deserves, though not by much. After the plans are laid Telemakhos is left with all the dirty work, gathering the suitors weapons and such, while his father gets an idea of the suitors strength. Telemakhos does very well in gathering the arms, keeping the suitors busy, and holding his temper at the mistreatment of his father in his own home. He acts very mature, having learned from the best sources in the land, and keeps a very cool head. He has most definitely changed from the young boy he was.
Telemakhos does equal his father by the end of the book. By almost stringing the bow that only Odysseus could string and only letting the knowledge that it would destroy his father's plan stop him from stringing it all the way he shows that he can do whatever his father can. He may not be the same level of planner yet, but he obviously posses the strength and wit of Odysseus.
It is also clear the Athena favors him as she does his father, helping Telemakhos in every way she can as she did for Odysseus. She is the one who originally gave him his courage and led him to learn from Nestor and Menelaos. She guides him along every step of his journey to manhood. She assists both him and his fathers in the fight with the suitors, letting them triumph over almost unbeatable odds. Without her help, it is questionable if they could have won over so many.
Telemakhos changes greatly during the course of the Odyssey. He matures, grows smarter and wiser, and becomes much more like his father. He learns much from his Nestor, Menelaos and Athena, but when Odysseus returns home he is finally able to take the place that he had wanted for so long. He is finally able to become Odysseus' son, and truly his father's equal.

Works Cited
The Odyssey, Translated by Robert Fitzgerald ?1989 Benedict C. Fitzgerald