Willing union of states and UN membership

Question

Consider the following three scenarios, separated by their initial state of affairs:

1. Distinct states A, B are recognized UN members.
2. Distinct states A, B are a UN member and a non-UN-member state
3. Distinct state A is a UN member state and B is a territory not recognized as part of any other state, but whose political situation is complicated, unstable, in conflict among UN members etc.

And suppose that A, B are territorial neighbors; of a similar size geographically and of similar population size; and that there's no third state stuck in the middle between them or other such complications.

Now, beginning from one of these three states-of-affairs, suppose there arises a movement for unification of A and B, with wide support: A's government and parliament take appropriate decisions supporting the union, and in B, whatever political mechanism exists does the same. And there are also strong indications of public support, e.g. internationally-well-regarded opinion polls, large demonstrations etc.

What would need to happen, formally in the UN, for a unified A+B state to be recognized/accepted as a member? And how would this be affected if the unification happened "on the ground", i.e. if a single unified political entity emerges, even while a government-in-exile of A continues to exist abroad and has a UN delegation?

Notes:

• I realize the scope of this question may be a bit wide - but am not sure quite how to narrow it usefully; if you can answer for a narrower scope, please suggest the narrower scope in a comment.
• If I get decent questions here, I'll have a followup question about "reluctant" unions.

Answer 1

The process of recognizing the existence of a state is fundamentally a political process, and admission to the U.N. or any other action one might take is simply on chit in the process of making a political case.

Ultimately, membership in the U.N. does not compel another country to recognize your state, or to recognize a particular regime as the legitimate government of your state. The decision of one state regarding which countries are legitimate sovereign states and which regimes are the legitimate rulers of those states is ultimately up to the political and legal processes of the state faced with a decision to recognize it or not, and the decision is far more political than legal.

If one state, say China or the United States of America, doesn't want to recognize the existence of another governmental entity that controls territory, say Taiwan or the Confederate States of America, it doesn't have to and nothing can compel it to do so.

What ultimately matters is whether the other states that a regime would like to deal with recognize it for the purposes that the regime seeking recognition would like to receive, and what the "reality on the ground" is among the people who live in the territory that a regime claims to rule.

So, rather than looking for an answer to this question, it is more useful to recognize that legally, it has no meaningful effect.

Ultimately, the recognition of sovereign states is a political rather than a legal matter, and likewise, very little of what is called "international law" is binding law in the sense that domestic statutes are binding law.