Ergo Proxy is the proxy form of Vincent Law, he is the proxy of death since his reference to himself as quote "I am Vincent Law, the Agent of Death." Ergo Proxy is also Proxy One and Proxy One is Ergo Proxy however Proxy One created Ergo Proxy that is why he refers to Vincent as his shadow.
Ergo Proxy is the creator of the dome Romdo, a utopian civilization where humans are aided by AutoReivs for their everyday necessities. The proxy Ergo is viewed as the dome's God and a required factor for the its continual existence.
Through a series of events, Ergo Proxy leaves Romdo for Monad, the Proxy of Mosk, whom he's has fallen in love with. For this reason, Mosk is destroyed and Monad is taken back to Romdo. Before leaving Romdo, Ergo Proxy appointed it a human regent known as Donov Mayer.
As a form of denial to the recognition that he is a flawed god and has created flawed beings, Ergo Proxy conceals his past memories in the form of amnesia, thenafter leaving Mosk as Vincent Law, his human form. Along with refugee survivors, he heads to Romdo and begins to work as an immigrant, working hard to become a fellow citizen.