None of the countries was recognized as the sole successor of Socialistic Yugoslavia. Each of the republics had to apply for a new membership.
Arbitration Commission of the Peace Conference on Yugoslavia issued the following opinion (No. 9) on the state succession:
[The Commission] ruled that it should be resolved by mutual agreement between the several ...
There are two competing principles in international law.
Nations have a right of self-determination.
Nations have a right of territorial integrity.
The obvious problem comes up when part of a nation declares itself a nation and wants to secede. If they are a People with a capital P within a multi-nation state, then self-determination may win. If they are ...