This console command sets ownership of the item you have selected as a target to the specified NPC or faction with the specified base ID (see argument information and examples for help). To select an item as a target, drop it on the ground and click on it whilst the console is open. If your target is a container, all of the items inside the container will have their ownership changed.
setownership [npc base id / faction id] Target Command
| NPC Base ID / Faction ID | Enter 'player' (without quotes) to make your character the owner. Enter the base ID of an NPC to set an NPC as the owner of the item. Enter a faction ID to set a faction as the owner of the item. |
setownership player
The above command would change ownership of the item you currently have targeted to you (your character would own the item). If a container (not an item) is your target, this would make your character own all of the items in that container.
setownership 1F259
The faction ID for 'College of Winterhold' is '1F259'. This command would change ownership of your current target to College of Winterhold.