Having 25+ rep with both Paranid factions I could, of course, simply do nothing and leave Duke to his own devices after delivering his fleet and carry on happily mining and selling ships to all sides ad infinitum. But where's the fun in that, I say.

On the other hand actually helping Duke puts me at war with the owner of by far the most important mining ground in the region and the source of about 50% of the resources required by my industrial centers located in GE, BHS and 18 Bn.

This presents a strategic dilemma because securing Pious Mists II and IV (meaning obliterating the Paranid presence there) involves necessarily physically separating the HOP from the Paranid which seems contrary to the whole point of this exercise.
So, I don't actually know what Duke does after triggering the final act of this plot, or what he might be capable of doing should I elect to assist him. I have run the game for a short while following triggering the fleet delivery just to see what happens and it seems he just starts attacking the Paranid stations in Duke's Haven and more or less loses all his ships in so doing. Disappointingly, although I built him a whacking great shipyard and he has subsequently built a large number of stations mimself, I see no evidence as yet that he is building large numbers of ships with which to service the hoped for rampage across the southern Paranid sectors.

I could, of course pull out of Pious Mists altogether and relocate my PHQ (which hosts my shipyards) more or less anywhere since all my main production facilities have 5* managers etc, and exploit new replacement mining grounds up north perhaps. But I'm not sure I can be arsed to do that. Not without significant motivation anyway.
So the question really turns on what Duke is actually likely to do and what, with my assistance, he is capable of. Being able to build as many Asgards, for example, as I like and observing from taking a couple of them for a test drive in Scale Plate Green that they can 1-shot a K with 60% shields and 100% hull I am in a position to obliterate the Paranid from Duke's Haven in a jiffy and thus preserve Duke's starting battle fleet. I could also clear Pious Mists II without difficulty.
The questions I have therefore are basically:
a) WIll Duke actually use his shipyard to build more ships?
b) Will Duke expand and take over Pious Mists II and beyond?