In the Civil War plotline of Skyrim, a lot of attention is paid to whether or not Skyrim has a right to self-rule. Typically, in a feudal society, a nation doesn't enter into a federation, a noble enters into fealty with another. Do we have any concept of what agreements were made to Tiber Septim? If, as what would likely have been the case in our world, the High King of Skyrim swore fealty to Tiber and his heirs, upon the death of Martin Septim that oath becomes null and void, and the High King of Skyrim became beholden to nobody. By my understanding, Mede crowned himself Emperor just for taking the Imperial City; do we know if the High King renewed his oathes to him?

Legally speaking, what's the status of Skyrim?

There doesn't seem to be any real question of the legitimacy of the Mede dynasty; no one seems to be actively challenging them. Falk Firebeard pointed out, that if Queen Potema returned from the dead, she would be the only living Septim -- the implication being that she would challenge the Medes.

It's fairly clear that High King Torygg was loyal to the Empire, and presumably there was some sort of formal recognition of that when he or the current emperor was crowned (whichever came first), that being the sort of thing that gets included in such rituals; it would have been conspicuous by its absence.

I haven't followed the Stormcloak quest line, but I don't have the impression that Jarl Ulfric makes a point of the Mede dynasty being illegitimate. I don't think that's a point he'd omit if he thought it would play.

Potema would be crowned Empress, according to Falk the second she would return to life. This does sort of imply that the Septim Empire is still considered to be for the Septims, and that any other dynasty can rule in their absence, which considering the fact that the Septims are all gone, could be quite long.
Ulfric never makes a point of Mede his legitimacy, so it's likely that nobody cares. What we've seen through earlier times when the royal family completely died out seems to suggest not so much an oath to a person but to an institution, and that oath lasts long after the death of one or all of their rulers.
The fact that none of the provinces immediately left the Empire seems to suggest the same to me, sure Elsweyr, Black Marsh, Hammerfell, Summerset have all left the Empire but not a single one did immediately after the Oblivion crisis which is when they had by far the best reason to justify doing that.

Well it was established lore-wise that Skyrim was one of the first provinces to endorse Titus Mede as Emperor following the interregnum.

Also, legality is a meter of opinion. History is written by the victors. Ulfric wins - The Mede Dynasty were oppressors. Mede wins - Ulfrics rebellion had no merit and the only result of which was the loss of lives.

Personally I side with the stormcloaks, not necessarily with Ulfric. Mede did valiantly to repel the Thalmor invasion. But in accepting the white gold concordat he lost the respect of two of the most militarily significant provinces, Hammerfell and Skyrim. The time has come to let a more aggressive leader take charge. Nothing good can come of letting Thalmor Justicar's run rampant around your provinces for any more time than they have done.

If I remember right, the nords endorsed Mede too. Can't quite recall which book it was in though.

They did, but that was pre white-gold concordat

Indeed, but he wasn't talking about that. He wanted to know if skyrim ever swore fealty to the Medes.

I seem to be misunderstanding what you're getting at here.

He asked if skyrim ever swore fealty to the empire of the medes.

They did.

The white-gold concordat has no relevance on whether skyrim ever swore fealty to the medes.

They did. The medes then signed the White Gold Concordat, the situation in Skyrim became slowly untenable, Civil war breaks out. I was never disputing that they swore fealty. I was expanding on the current situation.

So the Stormcloaks are Now a bunch of Oath-Breaking dogs...

Well, if you do the Dark Brotherhood quest before the Civil War...

Feudal bonds were two-waystreets. The Stormcloaks can easily argue that the Empire failed to protect Skyrim from foreign enemies by allowing the Thalmor inside their borders, and hence the Empire were the Oath-Breaking Dogs to which the Nords no longer hold any fealty.