Thank You!
kH Splitting Offset is for proper hair interpolation around hair parting areas. It adds custom attribute to points, which is used later by kH Emit Hair, or kH Grouping compound. Emit Hait is doing a search for three closest UV points on guides, then it interpolates strands in between. If some of these points are on opposite side of line of parting, strands are interpolated in wrong way, like in last image. To prevent this, there is a way to 'cheat' ICE point locators, such as Get Closest Points, or Get closest Location node - at searching stage, points are grouped and moved to ensure that 'closest' point match to desired groups of hair. After taking attributes, points are moved back to their original positions.
Also, there is general styling purpose for splitting offset groups. In image, IDs, created by searching for closest location on 'subcurves point cloud', were used as splitting offset value.
With Kristinka Hair nodes, both kH Emit Hair and kH Grouping compound are doing a search from UV point at emitters (instead from point position, as in PhilPack), which means this value, after conversion to 3d vector, is always somewhere inside point cloud's XY 0-1,. Splitting Offset value is able to change this (only at searching stage).
Modifiers such as Follow NURBS are able to set it's own splitting offset value, but this isn't enough when some parts of NURBS surface, used for modifier, are close to each other. For this case, kH Splitting Offset node is able to take modifer's UV, and create 'splitting groups'.
In image bellow, this somewhere in middle of Y(V) of modifier's NURBS surface. Another way may be using two modifiers on same NURBS surface, like before the last update, which isn't so convenient.
Previous version from September had a very limited way for proper splitting, dependent on shape of NURBS emitter. First version had alomost nothing. I've tried some automatic way, where every modifier adds splitting value to result of previous, but this wasn't enough, so there is a separate node, also values in modifier's PPG. Now it's possible to create splittng groups by weighmaps on emitter or influence nulls.
When using only one point cloud, all that Splitting Offset story has effect only when using kH Grouping node.
By the way, Softimage hair system has a way to do splitting that 'overlaps', which looks strange in viewports, but seems to be a nice option for covering the hair parting lines in rendering. I have a few nodes that doing something similar, but nothing as a definite solution, for now.
Cheers