So it was something of a surprise to find her giving a Commons statement on her return.
Is "her" collocated with "to find" or with "giving" in the sentence above?
"Her" is the direct object of the infinitive "to find". "
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"Her" is the direct object of the infinitive "to find". "Giving a Commons statement [up]on her return" is adjectival, modifying "her." "On her return" is adverbial, modifying "giving."
'find' is a complex catenative verb. It takes a verb in -ing.
The intervening NP is associated with both 'find' and the -ing verb, but in different ways, so that it says, in effect,
... to find her/she was giving ...
'her' is thus the object of 'find' and the subject of 'was giving'. I don't know how 'modern grammarians' resolve the dual nature of 'her'