Now at the MMD Mechanical Music Media web site:

  Fats Waller Rollography, by John Farrell
  THE PIANO ROLLS played by THOMAS WALLER and "FATS" WALLER

Some excerpts from John's introduction:

"During the years 1923 to 1931 twenty-three piano rolls marked 'played
by Thomas Waller' were released on the QRS label.  These rolls, bearing
Thomas Waller's signature in facsimile, were hand-played by Waller
although some, if not all of them were edited by J. Lawrence Cook.

"In 1935 QRS started producing rolls marked 'Played by "Fats" Waller'
(or 'Played by Thomas "Fats" Waller').  These were in fact played by
Cook, many executed in excellent Waller style.  As Fats was both
impressed and pleased to hear how Cook was able to imitate him, he
gave permission to have his name used on the rolls."

See John's thoroughly documented research and roll lists at

  http://mmd.foxtail.com/MMMedia/  (click on "Rollographies")
  http://mmd.foxtail.com/MMMedia/rollograph.html
  http://mmd.foxtail.com/MMMedia/fatswaller1.html

The document is also at Ian McLaughlin's website, which you can reach
at http://www.pianola.demon.co.uk/  (click on "Music Roll Artists").

Robbie Rhodes, MMD