Signing over rights to children

Do you think that if someone is asked to sign over their rights to their child, they should still have to pay child support? 
Do you think that a parent who is not allowed to see their child at all should have to pay child support? 
If one parent wanted to terminate the pregnancy and the other did not, should the parent who wanted to terminate have to pay child support? 
Sorry about all the questions. I'm just curious to know where people stand on this topic. 

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