State appellate courts serve as intermediaries between

The answer is High courts and trial courts. 

It can hear cases on appeal and the authority of the Supreme Court is the highest power of an appellate court. The functions of the appellate court can vary depending on the rules.

Explanation:

High court normally applies to the superior court (or supreme court) of a country or kingdom. In some nations, it is the highest court (for example, Australia). In others, it is located lower in the bureaucracy of courts (for example, England and Wales). A person who controls as a judge in such a court may be called a High Court judge, or, in some instances, a High Court Justice.A trial court of common jurisdiction may detect any public or criminal case that is not previously completely within the power of another court.

separation of powers, therefore, refers to the division of government responsibilities into distinct branches to limit any one branch from exercising the core functions of another.   the intent is to prevent the concentration of power and provide for checks and balances.  

the traditional characterizations of the powers of the branches of american government are:

* the legislative branch is responsible for enacting the laws of the state and appropriating the money necessary to operate the government.

* the executive branch is responsible for implementing and administering the public policy enacted and funded by the legislative branch.

* the judicial branch is responsible for interpreting the constitution and laws and applying their interpretations to controversies brought before it.

forty state constitutions specify that government be divided into three branches:   legislative, executive and judicial.   california illustrates this approach; "the powers of state government are legislative, executive, and judicial.   persons charged with the exercise of one power may not exercise either of the others except as permitted by this constitution."

while separation of powers is key to the workings of american government, no democratic system exists with an absolute separation of powers or an absolute lack of separation of powers. governmental powers and responsibilities intentionally overlap; they are too complex and interrelated to be neatly compartmentalized. as a result, there is an inherent measure of competition and conflict

minnesota:   minnesota house research,   separation of powers: when statutes and court rules conflict, 2005