Discuss Kurtz's use of the word "my" in Heart of Darkness. How might it reflect that which led to his downfall?
The answer to this question can be found through a careful analysis of what follows the quote that you refer to. One of the aspects of Kurtz's discourse that Marlow refers to and comments on is his propensity to use the word "my" and to claim ownership of all around him:
You should have heard him say, "My ivory." Oh yes, I heard him. "My intended, my ivory, my station, my river, my--" everything belonged to him. It made me hold my breath in expectation of hearing the wilderness burst into a peal of prodigious peal of laughter that would shake the fixed stars in their places. Everything belonged to him--but that was a trifle. The thing was to know what he belonged to, how many powers of darkness claimed him for their own.
The quote therefore suggests that in a sense, the tendency of Kurtz to claim everything that he saw as being his acted as a mask or something that blinded him to two crucial things. Firstly, the fact that he cannot own such items and nobody can, as is shown through the "prodigious peal of laughter" that Marlow waits to hear from the wilderness when he hears Kurtz claim ownership of nature so easily. Secondly, and most importantly, the biggest problem lies in the way in which Kurtz's ownership masks the far greater concern about who actually owns Kurtz's soul whilst he is so busy claiming ownership of those around him.