Need to replace a GUP in SEPm setup.

We have a single GUP (mostly win 2003 servers) at each physical site in our SEPm configuration.

We are building new win 2012 R2 servers to replace old win 2003 servers.

I have read doco and searched the forums but can find no specific information on how to replace a single GUP.

My instinct says that I can just name the new machine in the LU policy and that should take care of it, but seeing as I will be doing this on a live production system, I wanted to confirm that with some actual knowledge.

I am wondering if I need to withdraw the LU policy first, make the change, then push it again; but my instinct says that is too complicated and it should be as easy as my first though above.

I'd love to get some guidance.

Thanks in advance!

Trent.