Kyle Dixon:
The  buddhadharma never states that there is some 'thing' that  transmigrates. All that is ever occurring are causes and conditions  which proliferate ceaselessly.  
  "Therein, the aggregates are the aggregates of matter, sensation,  ideation, formations and consciousness. Those, called ‘serially  joined’, not having ceased, produce another produced from that cause;  although not even the subtle atom of an existent has transmigrated from  this world to the next."
-- Pratītyasamutpādakarikavhyakhyana
  
  and,  
  "Empty [insubstantial and essenceless] dharmas [phenomena] are  entirely produced from dharmas strictly empty; dharmas without a self  and [not] of a self. Words, butter lamps, mirrors, seals, fire crystals,  seeds, sourness and echoes. Although the aggregates are serially  connected, the wise are to comprehend nothing has transferred. Someone,  having conceived of annihilation, even in extremely subtle existents, he  is not wise, and will never see the meaning of ‘arisen from  conditions’."
-- Pratītyadsamutpādakarika