Does the word "all" function as an adverb modifying e prepositional phrase "over the floor"?Or is it a determiner or some other part of speech? Thank you.
1. Thanks to your question, I was able to learn something new about English grammar today.
2. I checked three sources.
a. The website Wiktionary feels that one should parse "all over" (as used in your sentence) as a preposition. Its example: "He dropped the bucket and got paint all over the floor."
b. L.G. Alexander's Longman English Grammar (1988), pages 151-152, parses "all" as an adverb that modifies the preposition in "Our baby went on crying all through the night."
c. Four respected scholars in A Comprehensive Grammar of the English Language (1985), page 685, give this sentence: "They splashed water (all) over me." The parentheses indicate that the authors feel that "all" is optional.
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In my opinion, "He spilled milk over the floor" does not sound natural. I feel that "all" is required in your sentence. Therefore, I personally would parse "all over" in your type of sentence as a preposition.