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The leaves fell to the ground one after another.
Literal
Tree-[possessive-の]-leaves [subject-が] one-after-another ground [on-に] fell.
次々と ('one after another, in succession') is a fixed adverbial phrase — 次々 (the reduplication of 次 'next') + the adverbial と. Describes a rapid succession of similar events. A vivid way to capture the rhythm of repeated motion in one compact adverb.