Pops who is that in your avatar?
Jim Anchower. He's an old "opinion columnist" from the Onion. I noticed that I was associating posters with their avatars so I went looking for one that matched me in spirit.
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I have only read the books once so I apologize in advance if I'm missing something obvious but I'm back to re-reading the series and an old idea popped up in my head: Gendry is the true son of Robert and Cierce.
First, I think it's physically possible. Cierce tells Ned that Robert got her pregnant once but she found a woman to take care of it.
Gendry seems to have received better treatment than Robert's other bastards (though it's hard to say for sure). He is apprenticed off in King's Landing by some mystery person. Notice that person is not Robert Arryn. The armorer knew Robert Arryn by sight but didn't associate him with whoever paid the apprentice fee; furthermore Robert never took an interest in any of his bastard children so it has to have been some third party who apparently didn't see fit to do this for all the others.
I think it fits the story arc in that the only Baratheon heir we are aware of is Stannis who has no sons of his own. There is no obvious male Targaryen heir (if Griff is indeed an imposter). Keep in mind that even if the theory surrounding John's parentage is true, he's still a bastard. Rhaegar was married when he scooped up Lyanna so they couldn't have married in secret.
Another telling sign is that an attempt was made to exterminate all of Robert's bastards despite the fact that they pose no obvious threat if they are all bastards. They went to some effort to chase Gendry down despite the fact he was headed to the wall. In addition, Martin has taken Gendry off the grid and out of the reach of anyone who has knowledge of his birth and who might wish him harm. Gendry is safely stowed away to reappear whenever it's convenient but he hasn't been forgotten entirely; we are more or less aware of his current location and situation.
Of course this raises questions. First, who would have apprenticed him off? My guess is Varys, although he had no obvious motive to keep him safe and alive at the time. He did keep Gendry within easy reach at King's Landing and for all we know, he was behind the idea to exterminate Robert's bastards to help clear the way for Griff.
Another obvious problem is that Gendry's status as the "true" son of Robert and Cierce is worthless unless somebody is aware of it. Stannis visited him with Robert Arryn but doesn't seem to believe Gendry is anybody important or he wouldn't be asserting that he is Robert's true heir (I think). It also seems that even if Varys is aware of it, he isn't going to be inclined to help Gendry.
So if I'm right I still have no idea how it would progress from here. Gendry needs somebody to tell him who he is and to find some compelling way to get others to believe in him and anyone who might have that information would have to know where to find him.
So maybe this is all nonsense or there is something I've forgotten that rules this out but thus far Martin has been careful to keep Gendry from knowing he's Robert's son. It seems there has been some effort spent here that would be useless unless there is a key point at which Gendry obtains knowledge of his father (at a minimum) and does something as a result.