What is the name of your state? Kansas If neither parent (never married) are considered custodial parent of the kid-- is custody up for grabs- can either parent get it, since they are both good parents one a minor the other legal age (just this year)? How does one go about getting the legal custody? I heard it's whom ever applies first? The child is shared between them right now while they finishing school and are working. Each lives with a parent of their own.What is the name of your state?