US state curtails child dumping - an odd law?

The BBC reports, at http://news.bbc.co.uk/1/hi/world/americas/7681139.stm that Nebraska has changed its laws - so that you can no longer 'dump' unwanted children on the state. The limit has been altered to only 3-days old - but before that it was 18 years - as the BBC site says:

The law allowed parents and guardians to leave children up to the age of 18 at hospitals without an explanation or interference from the law.

I must admit this seems rather extreme - but it did make me think: who 'owns' children and is responsible for them? Is it just parents - or all of us?