I agree with Andrei Volkov explanation, which follows to it's atthakathā. However, for the perfect understood by sutta, not only atthakathā, I write this answer.
- There is a reincarnation where one’s own intention is effective, not that of others. Atthi, bhikkhave, attabhāvapaṭilābho, yasmiṃ attabhāvapaṭilābhe attasañcetanā kamati, no parasañcetanā.
By atthakathā, above text refers to DN Brahmajālasuttaṃ:
- ‘And what is the second?
‘There are, brethren, certain gods called the “Debauched by Pleasure”
[155]. ‘For ages they pass their time in the pursuit of the laughter
and sport of sensual lusts. In consequence thereof their
self-possession is corrupted, and through the loss of their
self-control they fall from that state [156].
‘Now it might well be, brethren, that some being, on his
falling from that state, should come hither. And having come hither he
should, as in the last case, become a recluse, and acquire the power
of recollecting his last birth, but only his last one.
‘And he would say to himself: “Those gods who are not debauched by pleasure are stedfast, immutable, eternal, of a nature that knows no
change, and they will remain so forever and ever. [20] But we-who fell
from that state, having lost our self-control through being debauched
by pleasure-we have come hither as being impermanent, mutable, limited
in duration of life.”
By atthakathā, above text refers to MN kandarakasuttaṃ:
- There is a reincarnation where the intention of others is effective, not one’s own. Atthi, bhikkhave, attabhāvapaṭilābho, yasmiṃ attabhāvapaṭilābhe parasañcetanā kamati, no attasañcetanā.
Bhikkhus, which person torments others yoked to it? Bhikkhus, here a certain person is a killer of pigs, goats, birds, a hunter of wild animals, a fisherman, a robber, a highway robber, one who keeps a prison, or engaged in any other vicious activity. This person torments others yoked to tormenting others.
- There is a reincarnation where both one’s own and others’ intentions are effective. Atthi, bhikkhave, attabhāvapaṭilābho, yasmiṃ attabhāvapaṭilābhe attasañcetanā ca kamati parasañcetanā ca.
By atthakathā, above text refers to DN Brahmajālasuttaṃ:
- ‘And what is the third?
‘There are, brethren, certain gods called "the Debauched in Mind
[157].” They burn continually with envy [158] one against another, and
being thus irritated, their hearts become ill-disposed towards each
other, and being thus debauched, their bodies become feeble, and their
minds imbecile. And those gods fall from that state.
‘Now it might well be, brethren, that some [\q 034/] being, on his falling from that state, should come hither; and having become a
recluse should ‘as in the other cases, acquire the power of
recollecting his last birth, but only his last one.
‘And lie would say to himself: “Those gods who are not debauched in mind do not continually burn with envy against each other, so their
hearts do not become evil disposed one towards another, nor their
bodies feeble and their minds imbecile. Therefore they fall not from
that state; they are stedfast, immutable, eternal, of a nature that
knows no change, and they will remain so forever and ever. [21] But we
were corrupted in mind, being constantly excited by envy against one
another. And being thus envious and corrupt our bodies became feeble,
and our minds imbecile, and we fell from that state, and have come
hither as Being impermanent, mutable, limited in duration of life.”
‘This, brethren, is the third case.
- There is a reincarnation where neither one’s own nor others’ intentions are effective. Atthi, bhikkhave, attabhāvapaṭilābho, yasmiṃ attabhāvapaṭilābhe nevattasañcetanā kamati, no parasañcetanā.
By atthakathā, above text refers to DN Dānamahapphalasutta:
"Having given this gift seeking his own profit — with a mind attached [to the reward], seeking to store up for himself, [with the thought], 'I'll enjoy this after death' — on the break-up of the body, after death, he reappears in the company of the Devas of the Four Great Kings. Then, having exhausted that action, that power, that status, that sovereignty, he is a returner, coming back to this world.
"Having given this gift with the thought, 'Giving is good,' on the break-up of the body, after death, he reappears in the company of the Devas of the Thirty-three. Then, having exhausted that action, that power, that status, that sovereignty, he is a returner, coming back to this world.
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Why I have to link? Theravāda tradition never allow to explain tipitaka without reference, linking. It's weird and not professional. If buddhaghosa wrote something without the reference, he wouldn't be allowed to translate atthakathā back to pāli. So, the link, which I have given, show tipitaka memorizer's thought.