"The careful scholar might worry about plagiarism."
Andre Malraux argued that all artists begin with pastiche and only later develop a style of their own. Something similar is no doubt true of language in general. We learn a language by imitating how others use it. But we do not leave it at that. We develop our own distinct voice, which certainly betrays our "influences" but is nonetheless very much our own.
I came across Malraux's "formula" on the weekend while reading Harold Bloom's Anxiety of Influence. In that book, Bloom argues that something important happened to poetic influence after the Enlightenment. He would later revise that view, but it is interesting to note his distinction between art that is grounded in anxiety and art that is not. "Ben Jonson," he tells us, "has no anxiety as to imitation, for to him (refreshingly) art is hard work" (27). After the Enlightenment, however, the romantic "passion for Genius and the Sublime" made finding a style a matter of self-realization. It's still about "work", in a sense, but the "labour" has been rather radically transformed. Bloom quotes Kierkegaard: "He who is willing to work gives birth to his own father" (26). We might also recall the words of Borges: "every writer creates his own precursors".
Ironically, Borges's formula has become something of a slogan for aspiring academics (read: PhD students) who are struggling with what Bloom would call their "belatedness". Instead of taking it in Kierkegaard's sense, i.e., as the anxiety-provoking task of giving birth to your own father (!), they take it as a sort of "anything goes" principle. Whatever you write, they imagine Borges has taught them, a tradition will magically emerge behind them. After years of trying to get their tradition right, Borges's suggestion, not Jonson's, appears "refreshing". It doesn't seem all that hard.
Unfortunately, it is a least a little harder than that. My advice is to forget Borges (on this point) and stick with Malraux. After all, what they mean amounts to the same thing, but we are less likely to misunderstand Malraux. Begin with the awareness that your writing (at the beginning of your studies) is a pastiche of the things you are reading and commit yourself to the goal of developing your own style. Do not imagine that your writing will willy-nilly generate a distinguished line of precursors to serve as your tradition, in light of which your work will have some immanent "originality".
By the time you are writing your PhD dissertation, you should have mastered the art of pastiche, but if you don't make a conscious effort to do so you may never get beyond it. You need to find a way to present what you know in your own words. Here it is best not to imagine yourself the poet struggling anxiously with influence, but rather the scholar faced with the hard work of distinguishing what you want to say from what others have said before you. Think of it less as the "anxiety of influence" and more as the "worry of plagiarism". Be a little worried, yes, but don't get anxious.