Step 1: The clue word "potato tumor" identifies rhinophyma, a benign enlargement and disfigurement of the lower nose.
Step 2: Its pathological basis is overgrowth, that is hypertrophy, of the nasal sebaceous glands, often with connective tissue and vascular increase. It is considered the most advanced stage of acne rosacea.
Step 3: The bulbous nose looks ruddy because of dilated and engorged superficial blood vessels, and it predominantly affects older men. Alcohol is a myth rather than a cause.
Step 4: Management is surgical: laser, sharp excision, or dermabrasion with re-epithelialisation, or full excision and grafting. Sweat-gland and hypotrophy choices do not fit the sebaceous-gland pathology.
\[\boxed{\text{Hypertrophy of sebaceous glands of the nose}}\]