Either a lack of a publishing house name or a vanity press name that they pick. To my mind if I've never heard of a publisher before it is the same as saying "vanity press." I come to this belief after spending many of my college years working for a book publisher and many years of working with some of my wife's associates who publish their own books on sewing, quilting, and knitting.
So yes NatCh, the absence should be enough.
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