There is no formal doctrine of "child abandonment" in Washington and nothing to file that would create such a status. If you mean, "will the court terminate the biological father's rights and allow the stepfather to adopt?" the answer is, "maybe." It isn't a matter of years. It's a matter of serving the biological father with a motion to terminate his parental rights as part of the stepfather's petition to adopt. If the bio father consents, or is defaulted (for example, due to his failure to respond after being served by publication if he cannot be found) then, yes, his rights will be terminated. If he contests, however, then it becomes very difficult (but not impossilbe) to terminate his rights.
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