You are close, Sybe.
*kama asava can lead to existence in kama realms (four apayas, human, and six deva realms).
– When one does immoral actions to enjoy sensory pleasures, that lead to births in the apayas.
– kama asava goes away at the Anagami stage.
*bhava asava can lead to any existence. It is the desire to exist in a certain bhava or to attain a certain status. This goes away only at the Arahant stage.
*ditthi asava arises due to various wrong views. One can be born in the apayas due to wrong views.
– It goes away when one gets to Samma Ditthi, i.e., when one becomes a Sotapanna Anugami.
* avijja asava is due to the ignorance of the Four Noble Truths (or Paticca Samuppada or Tilakkhana)
– It is removed in stages and is completely removed only at the Arahant stage.