The two main characters, Vladimir and Estragon, have an undeniably intimate relationship. The mere fact that they have nicknames for each other, says a lot about the friendship. Though they vibe well and feed off one another, it is clear to see the power structure in the relationship.
One can easily see that Estragon is the dependent in this relationship. There’s an air of immaturity when it comes to him, and Vladimir is the one to help him get his act together (whether he wants to or not). Also, Vladimir is more of the emotional being than Vladimir who tries to use ration in situations. In the beginning of Act II, Estragon walks in on Vladimir singing, and though Estragon sees that as him being happier without him there, one can read that as to say that Vladimir has more independence and less reliance (one can contrast this with the opening of Act I when Estragon was met in the struggle of taking off his boots and needed Vladimir’s assistance). For the first few minutes of Act II, Estragon is almost like a child to teenage version of Vladimir. Vladimir has to be the one to remind of things, help him once again with putting on clothes, gets into an unwanted game of “Pass the Hat”, instructs Estragon on how to be a slave-owner (interesting that Estragon just didn’t take the role of Pozzo to show dominance, but showed dominance by telling him what to do), and then there was the quick failed game of ‘Hide N’ Seek’ from Estragon when he though Godot was coming (again interesting point to see him hide from the person he has been waiting so long on; almost like when a child has to interact with a stranger despite realizing that their parents know them). Similarly to a child visiting someone’s home, they are a bit more eager to go, especially when there is nothing to entertain them, this is the same for Estragon, as he continuously tells Vladimir that he is wants to leave.
It is clear that Vladimir sees himself as the watchman over and caretaker of Estragon and that carries out all throughout the play. In the biggest insist where Vladimir need Estragon’s help (them falling to the ground trying to help Pozzo up), Estragon failed, showing that the role of authority is not innate in him.