**Core Concept**
The condition described in the scenario is a classic presentation of a skin manifestation associated with HIV infection. The presence of multicentric skin lesions along with lymphadenitis points towards a specific type of skin cancer that is more common in immunocompromised individuals.

**Why the Correct Answer is Right**
The correct answer is Kaposi's sarcoma (KS), a type of skin cancer that is strongly associated with HIV infection. KS is caused by human herpesvirus 8 (HHV-8), which is a gamma-herpesvirus that infects cells of the immune system. In immunocompromised individuals, such as those with HIV, the virus can cause the proliferation of spindle-shaped cells in the skin, leading to the characteristic lesions of KS. The multicentric nature of the lesions and the presence of lymphadenitis are also consistent with KS.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because basal cell carcinoma is a type of skin cancer that is more common in fair-skinned individuals and is not typically associated with HIV infection.

**Option B:** This option is incorrect because squamous cell carcinoma is another type of skin cancer that is more common in individuals with fair skin and is not typically associated with HIV infection.

**Option C:** This option is incorrect because cutaneous T-cell lymphoma is a type of skin cancer that is characterized by the proliferation of malignant T-cells in the skin. While it can occur in individuals with HIV, the presentation is typically different from that described in the scenario.

**Clinical Pearl / High-Yield Fact**
Kaposi's sarcoma is a classic example of a "marker lesion" for HIV infection, meaning that its presence can indicate a diagnosis of HIV in an individual who has not yet been tested.

**Correct Answer:** D. Kaposi's sarcoma