you are right.. Linebreeding as you would to select for any other trait.. they breed the most Parthenogenetic hens with their sons, untill you get viable males, those males can be mate with their mother or systers....
to be more precise its called: Facultative parthenogenesis
Facultative parthenogenesis is believed to be a response to a lack of a viable male. A female may undergo facultative parthenogenesis if a male is absent from the habitat or if it is unable to produce viable offspring. This behavior...
there was a line of Highly inbrd Turkey breed that was bred fro that purpose, and some Males were hatched, they can only produce Males
here is the link
http://en.wikipedia.org/wiki/Parthenogenesis
sorry no males on those pics...
what you may see as fertile eggs are likely Parthenogenesis, but most of those eggs wont develope to become an embryo, I have a highly parthernogenetic hen that out of 10 eggs produced 1 single male. thats all they can produce males