  We give an explicit formula for the most likely path to extinction for the
Galton-Watson processes with large initial population. We establish this result
with the help of the large deviation principle (LDP) which also recovers the
asymptotics of extinction probability.
  Due to the nonnegativity of the Galton-Watson processes, the proof of LDP
verification at the point of extinction uses a nonstandard argument of
independent interest.
