Anyone think a captain can turn down a posting? Commander Riker refused his own command to stay with Picard. I would assume a Captain can do likewise.
I agree with you StyroFoam Man that a nobody has no choice, therefore I'd also think captains get really friendly with their fleet admirals, so as too improve their chances.
Of the Enterprise crew, Laforge, Data and Riker were all requested by Picard(not 100% sure on Data). As for Worf and Crusher, they came later in the series as replacements for lost crew members, Tasha Yar and that old doctor which I can never remember her name.
I think 'respected' Cpts get given a 'basic' crew and then have the leeway to assign anyone else they wish.
And that within reason the cpts choice comes first.
So he gets his PADD with 500 crew, desides he wants some of his old buddies onboard and gives them a call. Assuming they're up for it then transfer away.
Others request transfers, and obviously the likes of Riker and Troi XO/Counsellor go over the list. On a new ship/and or crew then the Cpt makes the choices and can no doubt veto any of his crew within reason.
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I would venture that a Captain, once selected for a posting, may submit recommendations for his senior officers. Whether or not those recommendations are accepted depends on the needs of the fleet, and on a given officer's current posting.
Starfleet also has the option of making a posting 'optional' or 'mandatory'. Most of Riker's opportunities have been optional - Starfleet would not want to take him off the Enterprise for anything less than his own command. Only Riker's renown keeps him on the A-list when new commands come up, but eventually he will run out of luck ... and a younger officer will be given the first shot.
Some additional leeway may have been granted Picard as the captain of the Enterprise ... perhaps one of the best known vessels in Starfleet. His recommendations may have carried additional weight as a result.
Narrators may also consider that command promotions will attract the attention of foreign intelligence services. If someone were to dust off Ben Maxwell and give him a ship patrolling the Cardassian border, you can bet the Obsidian Order would be assembling a crew roster before he left Spacedock.
For the most part I would have to say that the crew is assigned to the ship and the ship assigned to the Captain. Now, there are exceptions, Picard requested some members of his crew Riker for one and Sito Jaxa. Some like Dr. Crusher request their own transfers to the ship for one reason or another.
You don't want the crew getting too "close" otherwise you have officers like Riker, who IMHO will be lucky if he doesn't spend the rest of his career as a Commander after all the commissions he turned down.
Anyway, its like everything else in ST:RPG...its your game do with it as you wish.