This depends which editor you are using:
- **Potlatch** (on-line editor). I can think of two ways of doing this. (1) Select the junction node and then Shift-J should unconnect **all** ways. The node may change appearance to show that multiple nodes lie at the same point. You will now need to find the node belonging to the way you want to move and move it. Rejoin the remaining two nodes by selecting one and "J". This approach is a bit messy, but probably easier to understand. (2) Select the junction node and cycle through the 3 ways using the "/" key. When you find the way which does not belong to the junction "-" will delete **the node from that way only**.
- **JOSM** (off-line editor). Nodes can be 'unglued' using the "g" key press, again finding the relevant way and rejoining ways ("j") can be done as for Potlatch, but I don't know JOSM well enough to propose a more elegant approach. This video by Russ Nelson [http://www.youtube.com/watch?v=sjNlsBmLmYY][1] may be of some use.
[1]: http://www.youtube.com/watch?v=sjNlsBmLmYY