Split with auto-close curve?

Hi!
Is there a way to split (trim?) curves in a way that adds the splitter curve’s part of the split operation to the resulting curves?

Thanks!

CurveBoolean will do this. CombineRegions=No… (and maybe AllRegions, depending)

Thanks!
CurveBooleans indeed do the job (I wasn’t aware of the CombineRegions parameter), but there’s a catch: each of the areas has to be clicked manually, right?
That’s not feasible in this case, because what I’ve got is a rather complex map of nicely closed areas (derived from a SHP file out of QGIS), which I want to ‘split’ in the aforementioned manner, so that they remain closed.
image

I already managed to do this using hatches and trimming around manually, but still a quicker workflow would be interesting.
Cheers!

Not if you use AllRegions…

This is it! Thanks a lot!