Can one cut themselves off from a relationship with God?

Every great once in awhile there is a story in the newspapers, or on television news of a person going to court, after he or she becomes of age,  to legally sever the relationship with their adopted parents. 

Is something like this possible for us to do with God, our adoptive Father?

Or are we held captive in his family so that it is impossible to ever be seperated from Him?

Jesus said that He had not lost any that the Father had given Him. How does that play into the discussion of  “once saved, always saved“?

Can we just up and walk away from God…never to return…or be brought back?