I am reluctantly coming around to the view that maybe Archer Taylor got his overall conclusion (transmission from Britain to Scandinavia) wrong, but I still think there is considerable merit in his method. That was to look at various elements of the ballad, list which elements are in which versions, and then surmise whether any given element was more likely to have been in earlier versions and lost later or to have been absent in earlier versions and added later.

For example there is the difference between the mother's first noticing blood on the son's clothes or foot and then on the sword, versus noticing it on the sword straight away but being given excuses about hound, mare, etc. Did the mare's blood come first, transmogrifying into the horse or foals than Sven has been tending to, was it the other way round, or are they independent, present in the two different roles only by chance?

One feature (not known to Taylor) that I find striking is the consistent rhyming in that very old Swedish version versus a total absence of rhyming in most of the later versions.