Hi I am looking for any papers which extends the Turaev-Viro TQFT to a 3-2-1 theory (i.e. allows manifolds with corners) . I know this construction is known, but I cannot find a source. Please help.
As Charlie pointed out in comments Balsam and Kirillov were working on this, and since his comment they posted a preprint to the arxiv: http://arxiv.org/abs/1004.1533
For another point of view see Kevin Walker's notes in progress at http://canyon23.net/math/ In theory Kevin's point of view should automatically lead to a theory extended all the way down to points, but it's phrased in a different language from the usual extended field theory language.
This is a topic that people often say they're working on, but never seems to see the light of day. So, I wouldn't give much weight to off-hand statements that it's "known" --- it should be known, but talk is cheap!
There would be lots of exciting things to do with a well-presented extended Turaev-Viro model, so even if you end up duplicating other work it wouldn't matter so much, the fun would be just beginning :).