@feynhat Why do you get 3 markings on each bubble when you conpactify?

I don't follow your explanation by finiteness of the automorphism group. As far as I understand bubbling happens as follows: Take lines lying in P^1 # P^1bar (sitting in P^n) missing the blown up point, then take a limit as they tend to a line containing the blown up point, then the exceptional divisor bubbles out of your curve