How to join high current wiring?
Look for a "power distribution terminal block" or a "terminal bus bar." These are designed to land wires of various sizes and secure with a terminal screw, like the grounding terminals in your circuit breaker panel. Obviously you will need to ensure that the block or strip is insulated from other circuits as appropriate.

You may want to add crimp terminals/space lugs on the ends of your wires.

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Terminal bus bar, left; spade lug, right.