The correct answer is B) water-tube forced circulation. Auxiliary boilers are classified based on the type of water circulation within the boiler. The water-tube forced circulation boiler is one of the recognized classifications, where the water is forced through the tubes by a pump or other mechanical means, rather than relying on natural circulation. This allows for more efficient heat transfer and higher operating pressures compared to other boiler types. The other answer choices are incorrect because they do not accurately describe a recognized classification of auxiliary boilers. A) water-tube supercritical circulation and C) fire-tube controlled circulation are not standard boiler classifications. D) fire-tube express circulation is not a commonly used term for boiler types.