I think your question might need to be more specific to answer what you'd really like to know. In terms of states that were formed out of another state, I presume that it would be a near east state based on when large states developed, and the volatility of the large states in that region at the time (2000BC and earlier). The earliest I could find is Assyria gaining independence from the Akkadian Empire, though Assyria existed as an independent city state prior to being conquered by Sargon the Great. I would conjecture there were there were instances of states gaining independence prior to this, but are unknown to us.