Then someone else would need to be appointed and you and/or your siblings could likely apply for the position.
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If the administrator dies, or is unwilling to serve for any reason, the court will name someone else to serve as administrator. Courts may appoint surviving spouses, children, parents (if living), siblings, and grandchildren. You may ask the court to appoint certain people if you feel they would make a good administrator.
The estate administration will continue with the Court appointing another administrator as my colleagues have already stated. Assuming he has survived your mother by 90 days (or whatever term specified by statute to be considered as surviving her) before he passes, anything passing to him from your mother's estate will then pass through his estate.
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