If the square that the rebirth should take place on is occupied, either by a friendly or enemy piece, the captured unit is not reborn--it is instead removed from the board and takes no further part in the game (like a capture in orthodox chess).
The rules of circe chess were first detailed by P. Monreal and J. -P. Boyer in an article in Problème, 1968.
These are the most usual rules employed in circe - there are numerous other forms of the game in which the rules of rebirth may vary.
When notating a circe game in algebraic notation, it is conventional to place details of where a captured piece has been reborn in brackets following the move. For example, if in the diagram to the right, white were to take black's knight, this would be notated Rxe8(Ng8).
The position to the right demonstrates a couple of unusual effects which can occur in circe. It is black to move. White is threatening checkmate with 1.Re1#. Black would not be able to defend with 1...Kxe1 after this move, because the rook is instantly reborn on a1 from where it gives check (the fact that black's bishop defends a1 is of no consequence - after Kxe1 it will be white's move). It might appear that there is nothing black can do to prevent this threat, but in fact he has 1...Ba1! - if now 2.Re1+, Kxe1 is possible because the rook is not reborn owing to its rebirth square being occupied.
Circe is rarely played as a variant game (when it is, it is usually combined with progressive chess), but very often employed in composed chess problems.