A parent's sole purpose is to provide a proper upbringing to their children.
"Proper Upbringing" starts at birth and ends somewhere between ages 18 to 30. The difference between the ending age is completely dependent on how well a parent performs this task. I would think that 18 years of age is widely acceptable for a well developed child, some might think 16. On the other hand, 30 years of age as the maximum ending age, my opinion in this case, is probably widely debatable.
Once the child reaches the ending age the parent's responsibility to the child is finished. Whether they turn the child loose into the world, like the lion, or provide them with food and shelter for the rest of their life, everything that happens between the parent and the child is purely voluntary.