- Objective question asked and answered: admission as a state is by straight out Act of Congress.
This may take the form of a Bill or Joint Resolution depending on what it takes to get the votes through, and historically you do NOT “ride” it into a reconciliation or omnibus bill
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Number, order and timing of steps, ratifications, terms and conditions, transition process, etc. unless the specific matter has already been decided previously by statute or court precedent, are usually considered “political questions” for whichever sitting Congress to deal with as it sees fit, and have pretty much been handled as per individual circumstance for every state that has come along.
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Actually doing anything at all about the result of the vote is itself the biggest “political question” of them all, Congress is fully in its constitutional and political faculties able to just say “How nice. Thanks for sharing.”
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Political opposition to admission has been an issue as late as Hawaii and it does not have to be an R vs D thing - Most often it’s as a front for economic interests.
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Not asked but the 51 through 54 star flags have been designed for years, just in case.
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Not asked either but as to Seats: Before 1912, the House of Representatives simply expanded by an estimate of the required number of seats with each state admission and that new total was then reapportioned after the next census. Then the membership was locked at 435 and when Alaska and Hawaii were admitted in 1959, the House was* provisionally* expanded to 438 until the 1962 reapportionment could be done to revert to 435. If admission of Puerto Rico does not take place to coincide exactly with a Census it would involve 4 or 5 provisional seats until next reapportionment, or conceivably and as a way to garner votes, a permanent expansion of the total to 439-441 so no other state loses seats.
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With a population density of 980 per sq. mi. and having been Spanish-settled since 100 years before Englishmen settled Jamestown, it’s highly unlikely that there would be significant enough relocation into the island to effect fast anglification.
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And at this point we begin veering off into GD or at the very least IMHO territory, there being little else to be said about this that would be an objectively-answerable GQ.