TIL, when Pakistan broke off of India, the UN refused to automatically make it a member.

The United Nations Secretariat expressed the following opinion:

From the viewpoint of International Law, the situation is one in which part of an existing State breaks off and becomes a new State. On this analysis there is no change in the international status of India; it continues as a State with all treaty rights and obligations, and consequently with all rights and obligations of membership in the United Nations. The territory which breaks off-Pakistan-will be a new State. It will not have the treaty rights and obligations of the old State and will not, of course, have membership in the United Nations. In International Law the situation is analogous to the separation of the Irish Free State from Britain (sic), and Belgium from the Netherlands. In these cases the portion which spearated was considered a new State, and the remaining portion continued as an existing State with all the rights and duties which it had before.

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