Lets say I decide to capture someone I have disdain
for, so I set up a common trap where they board
my ship and then I remove them from the crewlist.
Now they haven't stolen from me or even threatened
me, but I feel they have wronged me in some way so
I keep them aboard the ship as a little pet. Now if I
did this would I me punish by admins, or does the
person simply get the opportunity to drop there
After three weeks they probably could petition the administrators and drop their toon if they wanted. However keep in mind that if you do this in some of the areas of controlled space the owners of that space will consider it a crime and they may come get you. They will then put you on trial and based on your posting here they'd find you guilty and you'd either be imprisoned yourself or executed depending on the government.
If it is done strickly IC, then I do not think the admins would get involved. If as you say you lay a trap and hold your victim prisoner, that is IC. As KU stated, you may be violating some law in some sector or another, either because of who you are imprisoning and their affiliation, because of where you are at, or maybe even due to you own affiliation. So should be prepared to face any consequences.
Now, with all of that said, good luck on your trap, though I doubt it will work since you've just advertised your intent.
Warning this is strictly Orions McPhees Opinion, it may or may not have any bearing on events true or imagined