The supreme court shall have general supervision of all courts of inferior jurisdiction to correct and prevent errors and abuses therein when no other remedy is expressly provided; it may issue writs of habeas corpus, of error, certiorari, mandamus, prohibition, quo warranto and all other extraordinary and prerogative writs and processes necessary for the furtherance of justice and the due administration of the law; it may entertain informations in the nature of quo warranto and petitions in equity to determine title to any office; it shall have jurisdiction of petitions for trials and new trials, as provided by law, of bills of exceptions, appeals and certifications to the supreme court, and special cases in which parties having adversary interests concur in stating questions for the opinion of the court as provided by law; and it shall by general or special rules regulate the admission of attorneys to practice in all the courts of the state.