How did Gandalf regain his staff?

[Valier]

I watched the Fellowship extended version yesterday, with this thread in mind. I stopped the movie just to check. Gandalf's first staff is a knarled wooden staff with a knobby top. After he looses it to Saruman, Gandalf is in Rivendell with a new staff. It is a different one. The one he has in Rivendell is a wooden gnarled staff, but the top is different. There are roots that come out one side of the top making it more elongated than knobby. (hope that makes sense) Then after he falls in Moria and is reborn, he has a white staff.

I think these staffs were probably given to him. Elrond would certainly have walking sticks like that or someone in Rivendell could make him one. Then surely in Valinor he was given a new staff to complete his mission.