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It would be similar to when your loan is sold. A new servicer would take over and you would simply send your payments to a new address.
Also, sometimes private investors will buy up the paper (your mortgage) for pennies on the dollar and than call you to offer you more favorable terms in an effort to keep you paying and protect their investment.
The most common answer is nothing. The servicing of your loan is the only part you would "feel" change through the process. The servicing rights are probably the only component of your loan held with Citi.