Facebook Father
Man whose sole contribution to the upbringing of his child consists of Facebook postings extolling his virtues as a father. A Facebook Father wants all the rights of fatherhood with none of the responsibilities and uses Facebook to fool the causal observer into believing that he is Father of the Year.
See also: Deadtweet Dad
That Facebook Father just posted a beautiful picture of his daughter, but hasn't paid child support, medical expenses or any tuition for over a year.