Admission of new states into the United States must be consistent with Article IV, Section 3 of the Constitution, but that leaves some discretion to Congress in a number of matters. What were the different ways of proceeding and which states were admitted according to which processes?
I know some examples of different ways of proceeding in the admission of states, but I also know my understanding is very incomplete, and I'm not sure any books deal with this question systematically. Examples:
With many states, the act of Congress said that the new state would be admitted when the president signed a certain document on a certain date, but with some other states, it simply said the new state would be admitted on a specified future date. With the first two of the states admitted under Article IV, Vermont and Kentucky, the latter procedure was followed.
Vermont and Texas make the transition directly from being a foreign country to being a state in the U.S.A. (Hawaii went through an intermediate period of some decades between foreign-country status and being a full-fledged state.) Vermont's de-facto independence was vehemently but ineffectually disputed by New York, and New York's governor George Clinton successfully campaigned against Vermont's admission for a long time; otherwise it would have happened almost a decade earlier under the Articles of Confederation (in a sense it almost did happen in 1781 but Clinton exerted great efforts to stop it, and did).
- Congress granted Texas the right to split itself into several states without any further action by Congress.
- In Vermont the state constitution that had already been in effect for years simply continued in effect with no changes at all when the state was admitted, and the governor and other state officers who were already in office under that constitution simply continued their terms of office without even so much as getting sworn in in the manner prescribed by the federal Constitution. (Might something similar have happened in Texas?)
- Kentucky was a part of Virginia until it became a separate state in 1792. Under Article IV, Section III, this required the consent of the legislature of Virginia, which was given in 1789. (I think governing such an extensive state was expensive and inconvenient and they also wanted more southerners in the U.S. senate.) Strangely, the act of Congress admitting Kentucky was actually passed two weeks before the act admitting Vermont, although Kentucky was not admitted until well over a year after Vermont. Because of New York's claim that Vermont was legally part of New York (although Vermont was under a government that refused to recognize that), Vermont could not be admitted until New York's legislature consented in 1790. Maine could similarly not be admitted (in 1820) without the consent of the legislature of Massachusetts (granted in 1819, I think?) and West Virginia was a strange case, admitted during the Civil War with the consent of some anti-secessionist legislators in Virginia.