What is the political status of each of the Tamriel provinces?
Solution 1:
My source is from Elder Scrolls Wikia and UESP.
- Empire: Skyrim*, Cyrodiil, High Rock.
- Aldmeri Dominion: Summerset Isles, Elsweyr, Valenwood.
- Argonian State: Morrowind, Black Marsh.
- Independent Provinces: Hammerfell, Skyrim*.
*Depends on player's choice on Skyrim's Civil War.
Though, because of the White-gold concordat, the Aldmeri Dominion has HEAVY influence on the Empire, meaning they have a 5~6 province influence on Tamriel
Hammerfell is the only province that defeated the Aldemri Dominion, and Morrowind and Black Marsh are the only provinces that still haven't been attacked.
A curiosity, is that, while in Skyrim, the Thalmor are considered "bad guys," in Elsweyr, they are considered heroes by the Khajiit For restoring the two moons of Nirn, and I haven't checked what Bosmers think of them.
Solution 2:
To correct the implications of the map included with @Ramirez' answer, I'm adding these maps that show the state of Morrowind based on available information during the events of Skyrim (Fourth Era).
Note that during the events of the Red Year (4E 5), the Argonians conquered southern Morrowind, but contrary to the map included by Ramirez, northern Morrowind still remains under the control of the remaining Great Houses of the Dunmer. The former Morrowind capital, Mournhold, has been sacked by the Argonians, and Blacklight (under House Redoran) became the new and current capital of Morrowind.
Sources: linked UESP wiki articles and in-game dialogue (Skyrim - Dragonborn DLC) of NPC, Adril Arano:
(click images below to view the higher-resolution, original image)
Source: "4th era geographical and political provinces" Dark Creations forums post by user, Lady Nerevar | darkcreations.org
Note included with the map: "Pretend that Solstheim is red, need to get around to changing that."
Also posted at the Imperial Library, "4th Era Tamriel - by Lady Nerevar" | imperial-library.info
Source: "TAMRIEL, political map, 4E 200" Bethesda forums post by user, L'eremita
Note included with the map: "After having seen many inaccurate maps I decided to read all the details found in Skyrim (and lore) and draw an accurately political map of Tamriel during the fourth era, 200.This map is "lore approved" as far as possible with all the information found. Enjoy, for all the lore fans."
"If someone liked it, I give the permission for use it on other sites, forums, wiki, other media and others encyclopedias of The Elder Scrolls universe."
Info about the other territories:
...in 4E 29, the Aldmeri Dominion was re-established across the Imperial provinces of Valenwood and the Summerset Isles, which were renamed Alinor. Once the Void Nights (4E 98-100) ended, the Thalmor (who govern the Aldmeri Dominion) claimed to have caused the return of Masser and Secunda. The Thalmor also developed a friendly relationship with the former Imperial province of Elsweyr in the form of two client states, Anequina and Pelletine. Later, in 4E 171, the Thalmor invaded Hammerfell and Cyrodiil after Titus Mede II rejected their Ultimatum. Aldmeri forces would push deep into both provinces, taking many cities, including the Imperial City. The Thalmor then faced their greatest defeat (later known as the Battle of the Red Ring), in which they lost all of their forces in Cyrodiil. Despite this, due mainly to the exhaustion of the Imperial Legions, the Great War ended with the White-Gold Concordat, which resulted in Talos worship being outlawed in the Empire and a significant portion of southern Hammerfell becoming part of the Dominion. However, Hammerfell rejected the treaty and left the Empire, continuing to fight the Thalmor until 4E 180, when the Second Treaty of Stros M'Kai was signed by both sides, resulting in the Aldmeri forces pulling out of Hammerfell and a territorial status quo.
Source: UESP wiki, "Aldmeri Dominion" article, which references the Skyrim in-game book, "The Great War"