when is a child emancipated going to college for masters?

Usually a child is emancipated at age 18, or after college if they go to college.  Whether or not a parent has to pay for a Master's Degree is usually up to the courts, and will depend on the finances of the parties, who paid for the college education, etc.  You have a very good chance of getting the child emancipated if she is going for a Master's degree.