Under German law you are required to pay child support until the child has completed his or her first full education, or until she is 27, whichever comes first. That means if the child wants to pursue advanced education the parent has to pay until she graduates from graduate school or turns 27, whatever comes first. If she does not pursue college and grad school, then the parent only needs to pay until the education is completed, which is either at the completion of "apprenticeship", which usually is 3-4 years after graduating from high school, or after high school in case no further education is pursued, but not before the child is 18.
But if the child choses to pursue further education even after completing one, the parent only has to pay if this education is a natural improvement of the first, for example:
Child graduates from high school and starts a paralegal apprenticeship. Then she decides to go to law school. The parent would have to pay through law school.
Example 2: Child does paralegal as above. Then child decides to study ancient history. Since this program has no logical connection to the first, parent only needs to pay until completion of the paralegal program.