I was told that you could place an add a newspaper re: Parental Rights and if the other parent never responded to the add that they would automatically sign over there parental rights. Is anyone sure if this is really valid or not.

You have to go through the court and they will attempt to locate and so forth.
You can not just take it upon yourself to place and then declare they are no longer the father because they did not respond.

Well if you are having an adoption hearing for a new partner to adopt the child, and if you have searched for the other bio parent because you do not know where they are. The Courts will have required searches to be done. Then you can post notice of the hearing, and the judge will normally take away the rights

But you can't do this, just so they won't know, if you know where they are at, they have to be notified.