I can't promise you they are the slimmest, but I can tell you that the highest volume of negative comments about how slim a model's neck was that I've read were directed to the early 2000s Memphis DOT reissue with the " '60s Slim Taper Neck." I happen to have a 2005 and experienced the onslaught of negative comments about the neck being way too slim. eace2 Perhaps that qualities. Now we are talking depth from front to back. The fingerboard is quite wide from treble to bass.
Bob