How does Wart's personality change in The Once and Future King?
You are right to place significant focus on the way in which Wart's character changes. One of the most prominent themes in this exciting and surprising Arthurian narrative is that of education, and in particular the way in which Wart's character develops and matures. Significantly, one important aspect of education that White stresses through the character of Wart is the way in which a close relationship and empathy with nature is presented as being so important to humans and the desired outcome of self-reliance. This is most clearly shown at the end of the first book, when Wart, facing his most significant challenge of having to remove the sword from the stone, pictures in his mind his varioius animal friends encouraging him to exert himself and to achieve his objective. It is this close relationship that Wart develops with nature that allows him to achieve self-reliance and to pull the sword out of the stone based on his own effort.
Therefore, when we think about how the character of Wart develops and begins to change, we can see how one very significant aspect of this process of maturity is the way that he begins to feel a much stronger sense of connection and kinship with nature, seeing himself as part of a cycle rather than separate to it. This of course is shown to lead to the all-important goal of self-reliance.