Assign

From Guild Wars Wiki

Assign means that a drop can only be picked up by the person it is assigned to. Items dropped from chests are dropped to the person who unlocked them. Items dropped by monsters are assigned to random member of your party. This includes henchmen and heroes, you just do not see the item drop, but the henchman/hero's chance of getting a drop is the same as a human character. (You do not get items that drop for your heroes.)