An in-depth analysis of the one dilemma that generates more rules questions than any other, Alien Parasites.

     Unless INTEGRITY>32, Away Team (if any) beams back and opponent immediately controls ship and crew until “stopped.”

Part 1 – How, exactly, does this work?
     First off, like most dilemmas, this one has conditions.  If your opponent has 33 or more Integrity, the dilemma is simply discarded and nothing happens.  If they have 32 or less Integrity, they fail the dilemma and the fun begins.  Set the dilemma aside while you resolve it.  If it’s the combo-dilemma, you need to reseed it for the REM Fatigue, but ignore the AP half of the card while it’s resolving.  The away team beams back (if encountered at a planet) and you gain control of their associated ship and everyone aboard.  The personnel who failed the dilemma are not stopped quite yet; you have to finish resolving the dilemma first, and the resolution is that you can now execute orders with the opponent’s crew.
     What can you do with the crew?  Pretty much anything you can do with your own personnel.  You can move them around by flying the ship and/or beaming.  You can attempt missions - the opponent’s or yours if they match the affiliation icons.  You can battle the opponent’s other cards if you can get around attack restrictions (like with Defensive Measures).  For the duration of the dilemma, it’s considered “your ship”, for things like Auto-Destruct Sequence.  If none of that interests you, simply beam down to a planet and strand the personnel, then attack them on your own turn.
     What can’t you do?  You can’t mix the personnel with your own cards, so you can’t dock at your Outpost, and you can’t beam the personnel to your ship / facility intending to strand them there.
     When the entire ship and crew becomes stopped, your control over them ends.  If you want to, you can simply yield control if you’re done using them.  If you do that, the personnel who failed the dilemma are all stopped, but any remaining unstopped crew (who were on the ship when the dilemma was encountered on the planet) will not be stopped.  This ship will only be stopped if the dilemma was encountered in space.
     If for some reason you don’t want control of the ship at all (say that Salta'na Clock will cause problems) you can immediately yield control and never take over the ship.  Once control is returned to the current player, then the Alien Parasites goes back under the mission, since it has conditions and does not say “discard dilemma”.

Part 2 – OK, what can complicate this?
     The biggest confusion is whether the dilemma has a trigger.  It does not.  Neither beaming up nor having a ship to control is required for this dilemma.  If they can’t beam up, you simply gain control of the away team on the planet.  If they are associated with a facility instead of a ship, they beam back to that facility and you gain control of the facility.  Since the dilemma does not target a ship, it’s OK to gain control of a landed ship.
     What happens if only some of the personnel get stopped?  You keep controlling the ship until everything is stopped.  If you use Distortion of Spacetime to unstop personnel, they are still under your control.  In fact, if there are other personnel on board who were already stopped, they’re under your control when unstopped.
     What happens if you get control of a docked ship?  Well, you’re stuck.  There’s no way to undock a ship from an opponent’s Outpost.  You can’t even beam off since that would include beaming thru the opponent’s outpost’s shields.  And yes, they still beam up thru those shields because you don’t take control until after beaming.

Part 3 – Making Parasites work.
     If you don’t care who you get control of, simply set it up with a big filter.  Chula: the Chandra and Hide+Seek work well, Blended isn’t bad either.  However, you probably want more than just one Redshirt, so the best filter is a wall dilemma exchanged with Beware of Q, with Hide+Seek in the Flash.  Shot in the Back or similar dilemmas can get rid of a single high-integrity personnel, but after just one killer, it’s possible to have enough personnel to still beat the Parasites.
     If you really want to control a ship with AP at a planet, put a Crisis in front of it.

Part 4 - Fun things to do with opponent’s personnel
     A simple trick is to just strand the personnel somewhere they’re vulnerable.  Strand the ship with no remaining range somewhere you can attack it on your turn.  Or strand it at Gaps in Normal Space.  Flying past Tetryon Fields is a reliable way to damage a ship without battling.
     Since the ship is now “yours”, there are 2 good combos to take advantage of that.  Hit it with Autodestruct Sequence or return everything to the opponent’s hand with Space/Time Portal.  (and then use Scorched Hand.  Or Masaka on your turn.)
     The best option is to attempt missions with those personnel.  If you play missions that have many icons, or “any crew may attempt”, then it doesn’t matter what affiliation you get control of.  You don’t care what dilemmas you run into (short of a Lack of Prep) because they’re not your personnel.  At the least, you get a look at a leading wall dilemma.
     You can also attempt your opponent’s missions.  That’s a good way to steal a few points.  The most popular combo is to put a dilemma after the Parasites that will cause problems.  Redshirt opponent’s personnel one by one into Armus: Sticky Situation, Chula: the Lights, or New Essentialists.  The opponent can’t Beware of Q swap your dilemma, so don’t worry about I Tried to Warn You.  A simpler way to get rid of everyone is to seed a Plague Ship and simply refuse to volunteer any Medical.  The downside is it requires you discard the TPS, where that Berserk Changeling would remain for when they return to that mission.  If you use Beware of Q to swap the Parasites when the opponent reattempts, maybe that flash will get rid of enough Security that they lose even one more personnel to the Berserk.
     Using the opponent’s personnel makes it easy to have the right affiliation to trip Dal'Roks or Sheliaks at other missions.  Or use Wormholes on the ship while it’s yours, getting around Operate Wormhole Relays.

Part 5 – Stopping the combos
     If you don’t want to get hit with AP at all, there are a few options.  Redshirting will minimize the damage.
     Try not to let the opponent have a ship.  Simply move your ship away and disassociate the away team.  You can prevent your personnel from beaming up with Atmospheric Ionization or Distortion Field.
     Fair Play will keep your missions from being stolen, HQ Defensive Measures will prevent an opponent from even attempting.
     Examine Singularity will let you get a Deactivation for Auto-Destruct Sequence after the ship is returned to your control.  Unfortunately, there’s not much you can do about STP except be ready with a Revolving Door.  Commandeer Ship will not prevent STP if the whole crew is under the opponent’s control.

Part 6 – the Borg factor
     What if you gain control of opposing Borg cards?  Well, you have all the same limits as a Borg player.  You can’t form away teams or battle or attempt missions.  Normally, those aren’t really bad limits, but with Alien Parasites that covers just about everything you could do with them.  You can move the ship, that’s about it.  However, it’s not a waste, since the fact that the drone beams back it makes this dilemma difficult to pass without Adapting.
     What if you’re playing Borg and get control of non-Borg?  Then you have more options.  You control them just as if you were not a Borg player.  You can attempt missions with them.  However, if you solve the mission, the points will be irrelevant to the Borg.
     If a mission is solved by a crew controlled with Alien Parasites, the dilemma is still re-seeded there.  That matters for Borg.  The mission may be solved, but it can still have a Borg Objective completed there, and the Parasites will be there when it’s scouted.