I tried that at first, but it doesn't return anything but the input line, not splitted. My query was badly written I guess.
I just made the most simple example I can think of and it works. The line still have to be exploded after to obtain distinct lines. This was not obvious. Other GIS I know do this in one step.
Also, in the Transform Toolbar, Intersect Lines requires lines in both input fields. This made me doubt about using the SQL extension.
So, to complete my query, I simply add a SPLIT BY Branches ?