What is a hyperfunctioning adenoma of the adrenal gland?

Secretory. An adrenal adenoma usually does not produce the usual adrenal hormones (corticosteroids or mineralocorticoids) but if does, it is called hyperfunctioning.
They do not function. Most adenomas are found by accident. They are usually asymptomatic and 2-5 cm in diameter and do not require therapy unless enlarging. One should then do blood studies to rule our pheochromocytoma. Which produces agents elevating blood pressure requiring Alpha and beta blockage. If removal required, best handled thru bed of 12th rib rather than an anterior approach used for large adrenal masses.

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Could you please describe hyperfunctioning adenoma of the adrenal gland?

Secreting hormones. Adrenal glands often get nodules/lumps/adenomas. They don't always secrete excess hormone. When they do, they can secrete aldosterone, norepinephrine, or cortisol. Each causes a syndrome: aldosteronoma, pheochromocytoma, cushing's. All include hypertension. If you have this, you should be seeing an endocrinologist.