H = PIE3MOD(HP) removes the lines along the edges of the pie slices while guaranteeing that there will still be a line separating the slices. The input argument HP is the set of handles returned by PIE3. The output argument H is the same as HP with the addition of the new line objects needed to separate the pie slices.
(Uncomment the code at the end of the file to move the slice labels in the front of the PIE3 plot so that they are beneath the pie's bottom edge. You may need to adjust the "thresh" value defined in the code depending on your PIE3 plot.)