They all seem to be adverbials, but none complements the object.
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How to distinguish the object complement from the pattern S+V+O+[prepositional phrase].This has to be done semantically, I think-- in any case, that is what I do. You have to understand the meaning of the prepositional phrase and decide to what it refers.
SelfconfidentIn this sentence-You can leave your case [with me]. Is this [prepositional phrase] the object complement?I think if the [preposition phrase] describes "where", "how", "who", 'what" and "when", it's function is adverbial.