**Core Concept**
Hyper-acute rejection is a rapid and severe form of graft rejection that occurs within minutes to hours after transplantation. It is primarily mediated by pre-formed antibodies against the graft, which are often present in the recipient due to previous sensitization.

**Why the Correct Answer is Right**
The organ most often associated with hyper-acute rejection is the kidney. This is because the kidney expresses high levels of the AB0 blood group antigens on its endothelial cells, which are also expressed on the surface of red blood cells. Individuals with pre-formed antibodies against these antigens, often due to previous sensitization or blood transfusions, can mount a rapid and severe immune response against the graft, leading to hyper-acute rejection. The mechanism involves complement activation and endothelial cell damage, resulting in rapid graft failure.

**Why Each Wrong Option is Incorrect**
**Option A:** Liver transplantation is not typically associated with hyper-acute rejection, as the liver expresses lower levels of AB0 blood group antigens compared to the kidney.
**Option B:** Heart transplantation can be associated with hyper-acute rejection, but it is less common than in kidney transplantation due to the lower expression of AB0 blood group antigens on heart endothelial cells.
**Option C:** Lung transplantation is not typically associated with hyper-acute rejection, as the lung expresses low levels of AB0 blood group antigens and is more susceptible to acute rejection.

**Clinical Pearl / High-Yield Fact**
To minimize the risk of hyper-acute rejection, it is essential to perform thorough cross-matching between the donor and recipient before kidney transplantation, including testing for AB0 blood group compatibility and the presence of pre-formed antibodies against the graft.

**Correct Answer: C. Heart transplantation can be associated with hyper-acute rejection, but it is less common than in kidney transplantation due to the lower expression of AB0 blood group antigens on heart endothelial cells.**