**Core Concept**
Centrosome duplication is a crucial process in cell cycle regulation, ensuring that each daughter cell receives the correct number of centrioles for proper spindle formation during mitosis. This process is tightly regulated by the cell cycle machinery to prevent errors in chromosome segregation.

**Why the Correct Answer is Right**
Centrosome duplication occurs during the S phase of the cell cycle, specifically when the cell is in the G1/S transition phase. This is when the centrioles, which are the building blocks of centrosomes, begin to replicate. The centrosome duplication process is initiated by the activation of the cyclin-dependent kinase (CDK) complex, which phosphorylates and activates the centrosome duplication protein kinase (CDK2). This leads to the recruitment of the Polo-like kinase (Plk1) to the centrioles, promoting the assembly of the centrosome duplication machinery. The duplicated centrosomes then separate and migrate to opposite poles of the cell, ensuring proper spindle formation during mitosis.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because centrosome duplication does not occur during the G2/M phase of the cell cycle. While centrosomes do duplicate during this phase, it is not the primary phase of centrosome duplication.

**Option B:** This option is incorrect because centriole separation, not duplication, occurs during the G2/M phase of the cell cycle. Centriole separation is a separate process from centrosome duplication, and it is essential for the formation of the mitotic spindle.

**Option C:** This option is incorrect because the G0 phase of the cell cycle is a quiescent phase where cells are not actively dividing. Centrosome duplication does not occur during this phase, as cells are not progressing through the cell cycle.

**Clinical Pearl / High-Yield Fact**
Centrosome duplication is a tightly regulated process that is essential for proper cell division. Errors in centrosome duplication can lead to aneuploidy, a condition where cells have an abnormal number of chromosomes, which can contribute to the development of cancer.

**Correct Answer:** C. The S phase of the cell cycle.