Quora is a question and answer site that I have never heard of before, but find fascinating. Apparently, it's a discussion site, not unlike the often-maligned Yahoo! Answers, where users ask each other questions and are encouraged to answer one another in often entertaining ways.
That said, in the hypothetical battles section of Quora—which makes me happy simply by existing—someone asked which American state would win, were they all to declare war against the others. Note that in this hypothetical, there is no foreign intervention in any way.
The first real occupation attempts happened when attempts were made to secure more assets.
The Republic of Texas sought to gain strategic advantages in the Central United States. To do this they sought to gain two strategic assets. The first was control of Whiteman AFB the home of the B-2 bomber program. The base was easily secured and the most coveted military bomber in the world was now in the hands of the Republic of Texas. The next was control of Colorado and her military installations of great value. Then finally was access to the Mississippi River. Two main offenses took place to do just that. The First Battle of New Orleans involved a massive force occupying the city to claim it as a port and artery for future engagements. In Colorado they met stiff resistance as many of the Texas military were unfamiliar with Mountain warfare. Colorado's major bases fell quickly since Colorado enjoys the smallest force to fight back the Texans, but they adapted an unconventional warfare stance that kept the Texans on edge for months. Still, at this point the mission behind taking Colorado had been achieved—control over its military bases and strategic assets. The insurgency does however slow down the growth of Texas.
New York pushed Northward. They pushed to claim all of New England and the food wealth they will need to supply their people now that resources from the Midwest are no longer available. The take over is mostly peaceful as many of the states have large, but mostly non-military populations. They encountered problems when large groups of refugees tried to flee to Canada and rioting ensued.
Illinois was calm. The Midwest Alliance grew steadily by seeking to secure the Great Lakes. They were able to take Ohio through a few fierce, but brief encounters. They also took on Minnesota and the mouth of the Mississippi River.
The West coast was now controlled by the two main powers—California with it's seat of power in San Francisco and The North East Union centered in Seattle. California gained support and taken control of all the states West of the Continental Divide and South of the Union. The North East Union pushed as far as Wyoming.
There is more—so, so much more—as the story tops out around 6,500 words, and it's worth a look solely to sate some morbid curiosity that one may or may not have developed amid the (empty) talks of secession that have been bandied about over the last few weeks.
For the record, Arizona has absolutely nothing of consequence to do in this potential war, being gobbled up by the "Californian Union of Democratic States." Take that as you will, rabid statists (which I assume is a more localized term for nationalists).