Which branch of gov’t has the power to create all the lower courts (courts inferior to the supreme court)?

The branch of government that has the power to create all the lower courts is the legislative. That is to say, the Congress. The U.S Supreme Court has the power to interpret the law and it was the one created by the Constitution. The Constitution also says that Congress can create lower courts over time.

The judicial Power of the United States, shall be vested in one Supreme Court, and in such inferior Courts as the Congress may from time to time ordain and establish.  

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