In the Odyssey, usurpation is a major theme. Ulysses is out there for seven years trying to make his way back to Penelope, and meanwhile a bunch of suitors have taken over his home in Ithaca and are impatiently waiting for Penelope to choose a new husband among them. When Ulysses finally returns home, he does so in disguise and slaughters the suitors one by one.
In Hamlet, another important text for Ulysses, usurpation is, once again, central to the story. According to the ghost of Hamlet's father, it was his brother Claudius that killed him and is now sharing the bed of Hamlet's mother. Hamlet is either driven insane by the news or feigns it for his own purposes, and like Homer's epic, the play ends with bodies everywhere.
Now if the only reason you plugged through nearly 800 pages of Ulysses was to read the bloodbath at the end – where Bloom stabs Boylan with a pair of antler's horns and throws him out the second story of 7 Eccles Street, and Stephen impales Mulligan with his ashplant – then you're going to be disappointed. This never happens.
But usurpation is a major theme in the novel. Mulligan is jealous of Stephen's genius and tries to cut him down to size by constantly poking fun at him. Stephen's last thought as he looks at Mulligan at the end of "Telemachus" is "Usurper" (1.356). For the hyper-literate Stephen, the usurpation theme makes him consider himself a Hamlet figure. Thinking of his Latin Quarter hat, he says, "God, we simply must dress the character;" later he thinks of it directly as his Hamlet hat (3.98). As we see in "Scylla and Charybdis," much of Stephen's theory on Hamlet comes out of his own family troubles. Like Hamlet, he wants to escape the fate of his father (drink and misfortune), and like Hamlet, he seems half-mad as he tries to find a way to get out from under the thumb of his usurper (the jealous Mulligan).
In Bloom's case, the usurpation is more obvious; Boylan is usurping Bloom's marriage bed by carrying on an affair with Molly. Yet whereas Ulysses is constantly trying to make his way home, Bloom is careful to avoid going home too soon in case Boylan has not yet left. When Bloom does arrive home, he finds that Molly and Boylan have made little effort to disguise their affair. Boylan's betting tickets are torn up in the kitchen, and their furniture is re-arranged so that Boylan and Molly could sit next to each other and play Love's Old Sweet Song. Unlike Ulysses, Bloom lets all of this happen (and unlike Penelope, Molly is a very willing adulteress). Instead of trying to stop the affair, Bloom searches for a way to reconcile himself to it and make his love for Molly compatible with the fact that she must go elsewhere for sexual satisfaction. In this case, Ulysses is more notable for its deviations from the Odyssey than its similarities.