Just how did Tiber Septim accrue the provinces of his empire?

Cyrodiil - Succeeded/Assassinated Cuhlecain.

Skyrim - ???

Highrock - ???

Hammerfell - ???

Morrowind - Treaty with Tribunal.

Summurset Isles - Giant Stompy Robot Attack.

Valenwood - ???

Elsweyr - ???

Black Marsh - ???

The Nords fell in behind him because they believed him to Ysmir, Dragon of the North.

TIber outright conquered High Rock.

Morrowind was brought in via agreement between the Tribunal and Tiber.

Valenwood was conquered.

Summerset was conquered.

Only the coast can be considered Imperial in Blackmarsh, the innerswamps were never occupied.

Elswyere was conquered.

Hammerfell was obtained through intervention on behalf of the Forbears against the Crown's, so semi military conquest, and semi invitation.

Don't forget the little detail that Tiber Septim used Numidium (acquired from Vivec and powered by the heart of the Underking) to conquer Summerset.

I thought Tiber took Elsywer not through armed conquest. Then again, I'm not that great with Elsywer history.

But the times that Tiber used his silver tongue to best other provinces were Morrowind, factored in with the fact that Reman I almost took over Morrowind and that Tiber was MUCH more powerful and savvy so Vivec took the best deal he and Tiber agreed too, and that Black Marsh was just way too dangerous to anyone to march into, so Tiber decided to nab it in name only. Not to mention it's soooo much easier to grab land when the enemy says "yeah, we'll join you, under these conditions you'll also like."

Moral of the story, don't go conquroring Black Marsh, unless you want 99% of your men dying from horrific diseases and end up suffering the Hist's revenge, and when meet with an equal, you meet on talking ground (Morrowind).

OP, this assessment is worth your time: http://www.imperial-library.info/content/rise-tiber-septim