Ser Malthred Stark, on 29 April 2012 - 10:10 PM, said:
He would have been in something similar to Renly's situation then. The way I view it is that the Targaryens were conquered, ending their rights to the Throne.
If I steal someone's laptop, they do not stop having a de jure right to it. It is still legally theirs. Of course, if they/the police don't find me, then it is de facto mine. Theft does not legalise something. It just doesn't. If we accept that Kingdoms are different, and with enough people agreeing it does, then I really don't see the point to this topic.
Now -
I am guessing Robert's legal claim would have rested on
a) The presumption and belief that Aerys and his family have broken their vows of rulership, and that oaths of fealty to them are now null and void and then

In the absence of a king, a new one must be picked, and Robert had a reasonable blood claim and popular accord, for whatever it is worth
Now, if you accept this, then the right of legal descent remains in House Barethon, and if you don't Targaryen want their laptop back.
Assuming the former, descent obviously goes from Robert to children, then to brothers, then to whoever, excepting any changes in the will, which may or may not be legal anyway; considering that the Targaryens weren't above skipping people in the line of succession, I would consider them to be so. Its at this point that I can't remember what exactly the will said, which is annoying.
Personally, unless the will says otherwise and it may well have done, nobody's actually legally proved that Tommen isn't Robert's son. We all know reading the book, but to the average Westerosi, Tommen is the lawful heir until such time as he is disinherited for being not Robert's son. Unless the will as drafted by Eddard said straight to Stannis, which I think it might have, but can't remember, and am too lazy to look up.
And, of course, assuming the latter, than House Targaryen remain the lawful heirs to the Iron Throne. And the former or the latter really comes down to opinion, both in the book and out.
That's how I see it anyway. Three legal heirs, depending on which legal decisions you honour or not. Well. 'Legal'.