The plant with the world’s largest unbranched inflorescence is the titan arum, also called the corpse flower.
Its scientific name is Amorphophallus titanum, and it is native to the rainforests of western Sumatra, Indonesia. Botanically, the spectacular structure is an inflorescence—a cluster of many tiny flowers—not one giant flower. A tall spadix is wrapped by a large, pleated spathe.
When it blooms, the titan arum produces heat and releases an odor resembling rotting flesh. These features attract carrion insects that can pollinate its flowers. The bloom is brief, usually lasting only 24 to 36 hours, and the plant may spend years storing energy in its underground tuber before flowering.
The answer is sometimes confused with Rafflesia arnoldii, which has the world’s largest single flower. The talipot palm has a larger branched inflorescence, making “unbranched” the key distinction in this question. The titan arum first flowered in cultivation at London’s Kew Gardens in 1889.