Owning an object makes it special to us, and people identify objects they own faster than objects they do not; this has typically been assumed to be a general feature of object processing—that is, an object that belongs to you will be subject to a general advantage in processing by virtue of its ownership status. We show that, contrary to this assumption, this general processing advantage depends heavily on where the object appears; owned objects are not processed faster if they appear outside one’s own space. This gives important insights into how ownership and self-relevance, which are usually studied in simplified laboratory environments, might operate differently in more complex real-world environments where space itself can be owned.