**Core Concept**
During caecum surgery, various arteries are ligated to control bleeding and ensure a safe procedure. The arteries involved are typically branches of the ileocolic artery, which is a branch of the superior mesenteric artery. The correct ligation of these arteries is crucial to prevent post-operative complications.

**Why the Correct Answer is Right**
The correct answer is determined by the arteries that are typically ligated during caecum surgery. The ileocolic artery, which supplies blood to the caecum, appendix, and terminal ileum, has three main branches: the right colic, middle colic, and the ileocolic artery itself. The ileocolic artery is ligated to prevent bleeding from the caecum and surrounding tissues. The correct ligation of these arteries is crucial to prevent post-operative complications.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the ileocolic artery is indeed ligated during caecum surgery to prevent bleeding from the caecum and surrounding tissues.
* **Option B:** This option is incorrect because the right colic artery is a branch of the ileocolic artery and is typically ligated during caecum surgery.
* **Option C:** This option is incorrect because the middle colic artery is a branch of the superior mesenteric artery and is not directly involved in caecum surgery.
* **Option D:** This option is incorrect because the superior mesenteric artery is the parent vessel of the ileocolic artery and is not ligated during caecum surgery.

**Clinical Pearl / High-Yield Fact**
It is essential to identify the correct arteries to ligate during caecum surgery to prevent post-operative complications such as bleeding and infection. The ileocolic artery and its branches are critical to control during this procedure.

**Correct Answer:** C. The middle colic artery.