What were the final components of Greek spirits that controlled the fate of souls? 
Keres (mythology):  The Keres were daughters of Nyx, and as such the sisters of beings such as Moirai, who controlled the fate of souls and Thanatos, the god of peaceful death. Moirai:  Their number became fixed at three: Clotho (spinner), Lachesis (allotter) and Atropos (literally 'unturnable' but metaphorically 'inflexible' or 'inevitable' - i.e. death).
Clotho (spinner), Lachesis (allotter) and Atropos