Check out today's Honolulu Star-Bulletin for "Change in law gives panel new influence," a story about the Intermediate Court of Appeals, which is now the court of first impression for appeals-of-right in the Hawaii state court system. Until 2006, when the jurisdictional statute was amended to transfer primary responsibility to the ICA, the Supreme Court of Hawaii heard virtually all of-right appeals, and delegated a limited number of cases to the ICA.
The story explains the role of the ICA (it has six judges, and usually decides cases in panels of three), and contains short biographies of the current judges. It correctly notes the ICA is now the "workhorse" court which hears the first level of appeals, and the Supreme Court has become a (nearly) completely discretionary court, reviewing ICA decisions by way of an "application for writ of certiorari" (go here for an example).
The one thing missing from the story is the "transfer" procedure under Haw. Rev. Stat. § 602-58. Certain cases can skip the ICA, and the statute creates two classes of transferable case: those that "shall" be transferred (if the issue is one of "fundamental public importance," or calls for the invalidation of a part of the state Constitution, for example), and those where transfer is discretionary (issues of first impression, for example). A motion to transfer an appeal may be submitted after the filing of the record up until 20 days after the last brief is or could have been filed, which is why you often see briefs being considered by the Supreme Court bearing ICA captions. The latest example of a transferred case is the second "Superferry" appeal, which will be heard by the Supreme Court on December 18.