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In a comment, John Lawler wrote:

Grammarians often refer to them as "small verbs"; the implication is that they're in the process of change -- they're not really regular verbs any more, but they're not quite auxiliary verbs yet, either. Most of their meaning is bleached out, and they're each associated with a number of idioms, especially serial verb constructions, but there seems to be no single systematic pattern for their use that's evolved yet. See the various constructions cited in this freshman grammar exam question (#4 on the page).

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