**Core Concept**
The question requires the estimation of a hormone or substance that is involved in the pathophysiology of precocious puberty and hypertension in a child. The underlying principle is the relationship between the renin-angiotensin-aldosterone system (RAAS) and the mineralocorticoid pathway, which plays a crucial role in regulating blood pressure and electrolyte balance.

**Why the Correct Answer is Right**
The correct answer is related to the estimation of aldosterone, a mineralocorticoid hormone produced by the adrenal cortex. Elevated levels of aldosterone can lead to hypertension and hypokalemia (low potassium levels), which can contribute to the development of precocious puberty. Aldosterone promotes the retention of sodium and water, leading to increased blood volume and pressure. In children, excessive aldosterone production can be caused by conditions such as congenital adrenal hyperplasia (CAH) or aldosterone-producing adenomas.

**Why Each Wrong Option is Incorrect**
* **Option A:** Estimation of cortisol levels may be relevant in the diagnosis of Cushing's syndrome or other disorders of the adrenal cortex, but it is not directly related to the pathophysiology of precocious puberty and hypertension in this case.
* **Option B:** Estimation of sex hormones such as testosterone or estrogen may be relevant in the diagnosis of precocious puberty, but it does not address the potential underlying cause of hypertension.
* **Option C:** Estimation of growth hormone levels may be relevant in the diagnosis of growth hormone excess or deficiency, but it is not directly related to the pathophysiology of precocious puberty and hypertension in this case.

**Clinical Pearl / High-Yield Fact**
In children presenting with precocious puberty and hypertension, it is essential to consider the possibility of congenital adrenal hyperplasia (CAH) or other disorders of the adrenal cortex that can lead to excessive mineralocorticoid production.

**Correct Answer:** C.