How to have CTE query recurse parent query result one by one?
It does not seem possible to get control on how the recursion happens in CTE.

One solution to disentangle results is to add info on the parent query and build a 'path' for each result. 

As shown in this post:
How do I sort the results of a recursive query in an expanded tree-like fashion?

This seems to me the most acceptable way at the moment, but I'm still looking for a way to be able to directly get more concise results.