Relationships are an important theme in The Kite Runner because they provide much of the conflict and much of the resolution in the story. There are several sets of relationships that involve conflict and resolution, but let's focus on three major ones, the relationship between Baba and Ali, the relationship between Amir and Hassan, and the relationship between Amir and Assef.
The relationship between Baba and Ali is one of master and servant, but they have grown up together, which makes the relationship more complex. The two most important conflicts that emerge in the story are the fact that Baba had a relationship with Ali's wife that resulted in the birth of Hassan, an occurrence that is bound to create conflict between any two men, and when Amir accuses Hassan of theft, this creates a terrible conflict between the two men, resulting in the severance of their relationship. These conflicts are not resolved until after the death of both men, when Amir rescues Hassan's son, Sorhab.
The relationship between Amir and Hassan is fraught with conflict, even before Amir learns that Hassan is his half-brother. The relationship beween the boys is a master and servant relationship and also one of friendship. However, Amir is sharply envious of Hassam, well before Amir learns that Hassan is his half-brother. This envy and Amir's own deep insecurity and immaturity culminate in Amir's betrayal of Hassan when Hassan is assaulted by Assef and leads to the severance of the relationship between the two families. Only when Amir confronts his own demons and returns to his mother country does the conflict resolve, too late for everyone but Amir and his newly-found nephew, but still, a resolution.
The relationship between Amir and Assef is one of conflict from the beginning. Assef is a bully, and Amir is a coward, which provides a conflict that rules over Amir's emotions and deeds from the first time he encounters Assef until he finally faces him and refuses to give into cowardice toward the end of the story. Facing down Assef is what finally brings resolution to this tension in the novel.
THere are other relationships in the novel that provide conflict, for example, the relationship between the General and Amir or the relationship between Soraya and the General. The story is filled with conflicts between people that drive the plot and act as a powerful theme.