**Core Concept**
Parathyroid auto-transplantation is a surgical procedure where a diseased parathyroid gland is removed and reimplanted into another location in the body. This procedure is often performed to treat hyperparathyroidism caused by parathyroid adenoma or hyperplasia.

**Why the Correct Answer is Right**
The correct muscle for parathyroid auto-transplantation is the sternocleidomastoid. This muscle is chosen because it is easily accessible and has a good blood supply, which is essential for the survival of the transplanted parathyroid tissue. The sternocleidomastoid muscle is also located near the thyroid gland, making it a convenient site for the implantation.

**Why Each Wrong Option is Incorrect**
**Option A:** The pectoralis major muscle is not typically used for parathyroid auto-transplantation due to its location and blood supply, which may not be ideal for the transplanted tissue.
**Option B:** The trapezius muscle is not a common site for parathyroid auto-transplantation, and its location and blood supply may not be suitable for the transplanted tissue.
**Option C:** The submandibular gland is not a muscle, but rather a salivary gland, and it is not typically used as a site for parathyroid auto-transplantation.

**Clinical Pearl / High-Yield Fact**
When performing parathyroid auto-transplantation, it is essential to ensure that the transplanted tissue has a good blood supply to prevent necrosis and ensure the success of the procedure.

**Correct Answer:** C. sternocleidomastoid muscle.