It depends on whether you want 'look after' to mean 'take care of', which I assume you do. I'd analyse it as: [The boy]-SubjNP(or DP depending on what framework you use) [[looked after]-V [the sheep]-ObjNP]-VP with 'look after' being a phrasal verb.
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"Looked after" isn't a transitive phrasal verb, correct? For one thing, I can stick an adverbial between the lexical verb and the prep: Looked silently after. But I can't split it with the object as I think you can with a transitive phrasal verb: Hang up the phone. Hang the phone up.
This is not possible for 'hang up":
*Hang silently up the phone
My point was that "looked after" is a prepositional verb, not a phrasal verb as was suggested in the thread. I've been trying to understand the difference. It seems that many people are not aware that there is one.
Phrasal Verbs are easily distinguished from prepositional verbs.