lacking evidence to the contrary.  These days a DNA test is pretty conclusive.  Some jurisdictions would relieve him of responsibility...  others might not.  

One guy I know, was divorced, ex turned his child against him so child refused to see him for court ordered visitations.  After she milked all she could from said friend, ex-w got friend to sign off parential rights.  (I believe he was relieved of child support at that time.)  Ex-w got re-married & convinced husband #2 to adopt the child.  Marriage #2 didn't last & ex-h #2 had to pay child support on ex-husband #1's child.   Cute, Hunh?    

BTW, are you planning to do something really stupid?