In which biome would you find the tallest trees in the world?

rainforests

Monsoon Tropical region of South Asia. You can get a view of even thousands of tall (toddy) palms, over most of Deccan plateau & the adjacent coastal strips. South Eastern part of Deccan plateau is particularly dominated by this species, usually reaching fifty to sixty feet height.
In a gegraphically restrictive sense, the Temperate rain forests of North America's Pacific West (with very tall Redwood trees)

Hyperion, a Coast Redwood in California, at 115.5 m tall the tallest tree in the world, found in 2006. Hyperion is the name of a coast redwood tree in Northern California that has been confirmed to measure 115.55 m (379.1 feet), which ranks it as the world?s tallest known living tree.
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The main attraction of Redwood National Park is the coastal redwood (Sequoia sempervirens), one of the tallest trees on the planet. Along with Sitka spruce and Douglas Fir, these conifers form the dominant canopy of the coastal redwood biome, a distinct ecosystem that grows in the coastal fog belt of northern California.
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==> The answer you are seeking is: the coastal redwood biome!
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I hope this is helpful.

Redwood forest.