One of the tricky points. The common interpretation is Stephen paid the rent to the tower, and Mulligan is "usurping" the tower from him by taking the key. In real life, it was Gogarty who paid the rent; perhaps Joyce was taking some kind of revenge by reversing the situation.
An alternative explanation is that it is Mulligan who paid the rent, and what we read here is Mulligan's voice ringing in Stephen's mind. This would square better with the real-life situation, and the later revelation of Stephen's debt of nine pounds (more than twice his salary) to Mulligan.
