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Can someone tell me if it''s OK to say "I had John painting the house all morning" ?
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Yes, it means that you caused John (by threats, promises, or whatever) to be painting the house. It emphasizes the ongoing activity-- you kept John busy-- compared to the infinitive form ('I had John paint the house all morning'), which states John's assignment.

'Have' is a causative verb here, like 'make' and 'let'.