Legal Question in Business Law in California

On the California side, not much. You must maintain your California corporate formalities, including maintaining an agent for service of process in California. There are companies that specifically exist to be the agent for service for corporations. CT Systems comes to mind. You may already be using one, but if not you will need to. You will need to keep up your annual filings and taxes. Other than that, there is not much you need to do to remain a California corporation. There is no requirement that a California corporation have its corporate offices in California. On the North Carolina side, there are probably requirements that you be registered as a foreign corporation doing business in NC. You will need to ask a NC attorney about that.

Packing the boxes and moving. You'll have to register in that state and comply with whatever rules they have for doing business there.

If you take the advice of both previous answers, that'll pretty well cover it if you are really only moving the headquarters. As a practical matter, the business may have other related chores to handle, such as changing its letterheads, business cards, bank accounts, etc. and sending change-of-address notices to customers, suppliers, etc.

There's a possibility you are thinking of discontinuing your California business entity and forming or becoming an NC business entity. That's more complicated. It can be done (if the business is a corporation) by closing the CA corp. and transferring its assets and liabilities to a new NC corp., or by merging the CA corp. into an NC corp.

If this is more than just a move, and involves reincorporation, reorganization, etc., you'll need both accounting and legal help.