**Core Concept**
The extrinsic system of blood coagulation is a cascade of reactions initiated by the exposure of blood to tissue factor (TF), a transmembrane receptor that plays a crucial role in initiating the coagulation process.

**Why the Correct Answer is Right**
The release of tissue factor (TF) from damaged endothelium triggers the extrinsic pathway by activating factor VII (FVII) to its activated form, FVIIa. This enzyme then activates factor IX (FIX) and factor X (FX) through a series of enzyme-substrate interactions, ultimately leading to the formation of thrombin and fibrin. The extrinsic pathway converges with the intrinsic pathway at the level of factor X activation.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect as it does not accurately describe the initiator of the extrinsic pathway. **Option B:** Incorrect, as factor XII (FXII) is the initiator of the intrinsic pathway, not the extrinsic pathway. **Option C:** Incorrect, as platelet factor 3 (PF3) is involved in the intrinsic pathway and not the extrinsic pathway.

**Clinical Pearl / High-Yield Fact**
Tissue factor is a critical initiator of the extrinsic coagulation pathway, and its release from damaged endothelium plays a key role in the formation of a hemostatic plug.

**Correct Answer:** A. Tissue factor.