**Core Concept**
Port-wine stains are congenital vascular malformations characterized by a large, red, raised discoloration of the skin, often present at birth and persisting into adulthood. These lesions are typically composed of dilated capillaries and are usually unilateral.

**Why the Correct Answer is Right**
Port-wine stains are a hallmark feature of Sturge-Weber syndrome, a rare neurocutaneous disorder that involves the skin, brain, and eyes. The presence of a port-wine stain in the distribution of the trigeminal nerve, particularly on the face, is a diagnostic criterion for this condition. Sturge-Weber syndrome is caused by a mutation in the GNAQ gene, which leads to the activation of the MAPK signaling pathway and the development of the characteristic vascular malformations.

**Why Each Wrong Option is Incorrect**
**Option A:** Tuberous sclerosis complex is a genetic disorder characterized by the growth of non-cancerous tumors in various organs, including the skin, brain, and kidneys. While it can present with skin lesions, such as ash-leaf spots and shagreen patches, it is not typically associated with port-wine stains.

**Option B:** Neurofibromatosis type 1 is a genetic disorder that affects the development of nerve tissue and can cause a variety of skin, bone, and nervous system abnormalities. However, it is not typically associated with port-wine stains.

**Option C:** Klippel-Trenaunay-Weber syndrome is a rare disorder characterized by a congenital vascular malformation of the skin and underlying tissues, often accompanied by bony and soft tissue hypertrophy. While it can present with similar skin lesions to Sturge-Weber syndrome, it is not typically associated with the characteristic facial distribution of port-wine stains.

**Clinical Pearl / High-Yield Fact**
The presence of a port-wine stain in the distribution of the trigeminal nerve is a diagnostic criterion for Sturge-Weber syndrome. This condition often presents with seizures, developmental delays, and glaucoma, and requires early diagnosis and management to prevent complications.

**Correct Answer: C. Klippel-Trenaunay-Weber syndrome**