Taken from UOGuide: "Double-clicking on the character part of the statue will open a paperdoll of it. All items on the statue are generic, lacking any special properties. The status button is also disabled. Double-clicking the plinth will open up a plaque which displays the name of the creator, the date and time of creation, and the type of material. Statues are not account bound, and can be traded after being created. To demolish the statue, open a Contextual Menu on the character part of the statue and select "Demolish"."
And just in case you're worried about losing it, it also says, "After the first placement and demolish, it turns into a deed. The statue will stand on top of a plinth for prominent display."
Hope this helps!