What is the proceedure to become the administrator of the estate of someone who dies without a will?

The issue of whether or not you would have needed to sign a renunciation begins with your relationship to the decedent.   Let me explain by way of an imaginary family.  Lets say your aunt was one of four sisters: two of her sisters had children, but the decedent and another sister did not have children. either your deceased aunt's parents, or if they had died, her sisters, could serve as administrators of the estate.  Next step, lets say that one of the decedent's sisters had died before (predeceased) her.  that sister's children, if any, would then also be eligible to serve, and will be recipients under the intestate estate.  So in your case, if your aunt's sisters are all surviving, then the other sisters are the only ones that have to sign renunciations.  for example, if your mom is still alive, and she was one of your deceased aunt's sisters, then your mom would have to renounce her right to serve as administrator, but you would not have to because you would only have a right to serve if your mom has already passed.  I don't know if this answers your question.  the other possibility is that the assets your aunt owned all pass by operation of law, meaning there were Payable on Death (POD) designations, joint ownership, etc.  Essentially you are correct, if there were people who had to renounce, and they did not, then your aunt is most likely not the legally appointed administrator of the estate.