Posted by rfvv on Sunday, March 28, 2010 at 5:04pm.
Probably the last one is the closest. I've always taken that to mean "I am sincerely at your service." Sounds a bit weird, but then idioms usually are!
I don't think any of them is the full form.
Since "Sincerely yours" is used at the end of different kinds of letters, we don't assume that we mean either "friend" or "servant."
This site has a brief discussion of this term.
http://www.dailywritingtips.com/yours-faithfully-or-yours-sincerely/
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