What are the conditions for the transference (jar) of walaa' (patronage/allegiance)?

Primary text

The transference of walaa' is contingent upon three conditions. The first condition is that the father must have been a slave at the time of birth. If the father was free, but the mother was a freedwoman, no walaa' is incurred upon the child if the father was of free origin. If the father was a freedman, walaa' is established upon his freedman's patrons (mawālī) initially, but it is not transferred further (lā yanjarr). The second condition is that the mother must be a freedwoman. If the mother was of free origin, her child is free, and no walaa' is incurred upon the child. If the mother was a slave, her child is a slave to her master. If the master frees them, their walaa' belongs to the master who freed them, and it is never transferred from him. This is based on the saying of the Prophet, peace be upon him: "Al-walā' li-man a'taq" (Walaa belongs to the one who emancipates). Walaa' is established by direct emancipation and does not transfer from the act of emancipation itself. The third condition is that the slave (the father) must be emancipated by his master. If he dies while still a slave, walaa' is never transferred.