**Core Concept**
The adductor pollicis muscle is a deep muscle of the thenar eminence, playing a crucial role in hand function. It is one of the intrinsic muscles of the hand, responsible for thumb movement and stabilization.

**Why the Correct Answer is Right**
The adductor pollicis muscle is actually innervated by the ulnar nerve, not the median nerve. This is because the ulnar nerve supplies the intrinsic muscles of the hand, including the adductor pollicis, while the median nerve primarily innervates the thenar eminence muscles, such as the abductor pollicis brevis and the flexor pollicis brevis. The ulnar nerve's contribution to hand innervation is essential for proper thumb movement and opposition.

**Why Each Wrong Option is Incorrect**
**Option A:** The adductor pollicis muscle indeed has two heads: the transverse head and the oblique head. This is a correct anatomical feature, so option A is incorrect because the question asks for a false statement.
**Option C:** The adductor pollicis muscle does cause adduction of the thumb, which is a correct function of this muscle. This makes option C an incorrect distractor.
**Option D:** The arteria princeps pollicis is indeed the main arterial supply to the thumb, and the adductor pollicis muscle receives its blood supply from this artery. This makes option D an incorrect distractor.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the ulnar nerve's contribution to hand innervation includes the adductor pollicis muscle, which is responsible for thumb adduction. This is a critical anatomical correlation for surgeons and hand therapists.

**Correct Answer:** ✓ Correct Answer: B. Supplied by Median nerve