  We present results of a theoretical study of 4He films adsorbed on graphite,
based on the continuous space worm algorithm. In the first layer, we find a
domain-wall phase and a (7/16) registered structure between the commensurate
(1/3) and the incommensurate solid phases. For the second layer, we find only
superfluid and incommensurate solid phases. The commensurate phase found in
previous simulation work is only observed if first layer particles are kept
fixed; it disappears upon explicitly including their zero-point fluctuations.
No evidence of any "supersolid" phase is found.
