To remove the transfer case, ensure it is shifted to 2WD High, then disconnect the negative battery terminal cables. Raise the vehicle securely on jackstands and, if applicable, remove the transfer case skid plate by taking out the bolts. Drain the transfer case lubricant and remove the front and rear driveshafts. For manual-shift vehicles, take out the shifter and unplug the position switch electrical connector on top of the transfer case; for electric-shift vehicles, unplug the electric shift motor connectors. Support the transfer case with a jack, ideally a specialized one, using safety chains or tie-downs for stability. Remove the transfer case crossmember, disconnect the vent hose, and take out the bolts connecting the transfer case to the transmission extension housing. Ensure all wires and hoses are disconnected, then carefully move the transfer case and jack toward the rear of the vehicle until it is clear of the transmission, keeping it level. For installation, reverse the removal steps, ensuring to install a new mounting gasket and tighten the transmission-to-transfer case bolts to the specified torque. Fill the transfer case with the appropriate fluid, run the engine, and check for any fluid leaks.