One does not do a TRANSFER of the TIAA Traditional from an RA, and I assume from a GRA; one creates a TPA. The TPA is created as a separate account. Where the annual distribution goes is up to the participant of the TPA; it could be to an IRA or I assume the funds could be sent outside of T-C. In most cases I suspect the participant elects to have the annual distributions deposited in the IRA; this is what I did when I create mine (I have two) and what Dennis appears to have done.
One can change the designation where the annual distributions can be deposited at any time. I have not tried to specifiy a destination outside of my T-C IRA and therefore I cannot guarantee that is possible. But I have changed the designation of the annual distributions a couple of times and there is no problem in doing this. The funds remaining in the TPA do retain their vintages as Dennis said. The deposition of the annual distribution from the TPA in as far as I know, destroys the vintages one the funds are distributed including when the annual distribution is placed in the Traditional Account in the IRA; again Dennis is correct.
You can do this at any time and therefore you have lots of choices where to place EACH annual distribution. You can put in in the Traditional Account in the IRA for one or more years, and then change it to the MM Account or the REA or the ILB, etc. And the following year you could change it again. If I remember correctly I have changed it twice in one year! :-)
IF you want to annuitize ANY PART of the funds remaining in the TPA at any time you MUST ANNUITIZE THE TOTAL AMOUNT REMAINING IN THE TPA! Partial annuitizations of funds in the TPA are NOT permitted! Now, if you place the annual distributions into the IRA but in some account other than the Traditional Account, you can annutitize that amount into either a life annuity (single or two live with or without guarantee periods) but also into a TERM Annuity which most people would call a fixed period annuity. As I remember, though it depends on the age of the particpant doing the annuitization, the term period can vary from as little as two years to as much as 30 years.
Nothing Dennis said is incorrect. He just did not fully explain the nuisances.
Oh, one more point, if you have a TPA in place and become subject to RMDs sometime in the nine years and one day life of the TPA you cannot have T-C automatically do RMDs; you in effect have to do them manually yourself but as I (and Sy) have said elsewhere, this is not a big deal. IF you disagree with this statement you are welcome to check on it yourself but I warn you it is a bag of worms; I have been through it and I am convinced I am right on this.
Ray