> Haven't used --update-refs, but reading it, it should result in your third graph.

I don't think it does. I tried locally:

  mkdir test; cd test; git init
  touch a; git add a; git commit -m 'a'
  touch b; git add b; git commit -m 'b'
  touch c; git add c; git commit -m 'c'
  git checkout -b branched-feature HEAD~
  touch d; git add d; git commit -m 'd'
  git checkout main
  echo 'change' > b; git add b; git commit -m 'fix b'
  git rebase -i --root --update-refs

And ended up with this graph (`git log --graph --all`)

  * commit (HEAD -> main)
  |
  |     c
  |
  * commit 
  |
  |     b
  |
  | * commit (branched-feature)
  | |
  | |     d
  | |
  | * commit
  |/  
  |       b
  |
  * commit 
  
        a

Replacing the `git commit -m 'fix b'; git rebase -i --root --update-refs` with `git history fixup HEAD~` produces what I'd like:

  * commit (branched-feature)
  |
  |     d
  |
  | * commit (HEAD -> main)
  |/
  |       c
  |
  * commit
  |
  |     b
  |
  * commit 
  
        a

Huh.. That's a shame :(. Maybe what it refers to is if you had a branch on B rather than D, it might update that.

EDIT: Yeah, this seems to be it. `git branch b` on b, then `git rebase -i --update-ref @~3` from main caused branch ref `b` to move from d86229e to 02fcaf7:

  * 1e354fb (HEAD -> main) fix b
  * 40e6f70 c
  * 02fcaf7 (b) b
  | * f4188e0 (branched-feature) d
  | * d86229e b
  |/  
  * 5fe78fa a

> And ended up with this graph (`git log --graph --all`)

Add --oneline to get the compact version from the other reply.

It won't result in the third graph on its own as E isn't reachable from D, but it could if you first merged D and E together and then used --update-refs with --rebase-merges. You could then just discard the merged branch and only take care of D' and E' on their own (and since you don't care about the merged branch, you don't have to care about resolving conflicts while preparing it either).

Unless E remained untouched because it was not rewritten, and ended up staying parented on B instead of getting reparented onto B'.

Which is usually not what you want; most of the time you want E', which is E reparented onto B'. But sometimes you want E to remain untouched and stay parented on the original B. Depends on the situation.

Exactly, but the second graph where untouched E is reparented to B' is not something that git would allow.

Ah, good catch. That's more of a graphic issue and not what I was trying to express. Updated the OP.