When exactly did the “three generations” end?

بسم الله الرحمن الرحيم

قال ابن حجر رحمه الله في فتح البارئ:ـ
وقد ظهر أن الذي بين البعثة وآخر من مات من الصحابة مائة سنة وعشرون سنة أو دونها أو فوقها بقليل على الاختلاف في وفاة أبي الطفيل، وإن اعتبر ذلك من بعد وفاته صلى الله عليه وسلم فيكون مائة سنة أو تسعين أو سبعا وتسعين، وأما قرن التابعين فإن اعتبر من سنة مائة كان نحو سبعين أو ثمانين، وأما الذين بعدهم فإن اعتبر منها كان نحوا من خمسين، فظهر بذلك أن مدة القرن تختلف باختلاف أعمار أهل كل زمان، والله أعلم، واتفقوا أن آخر من كان من أتباع التابعين ممن يقبل قوله من عاش إلى حدود العشرين ومائتين

Ibn Ḥajar رحمه الله said while explaining al-Bukhārī (3650):
“And it has become clear that what is between the beginning of prophethood and the last one to die from the Ṣaḥābah is 120 years or a little less or more than that because of the difference (of opinion) on the death of Abū al-Ṭufayl. And if it is regarded after the death of the Prophet ﷺ then 100 years(1) or 90 years or 97 years. As for the generation of the Tābi’īn, if it is regarded from a hundred years then 70 or 80.(2) And as for those after them then if it is regarded from it then it is around 50.(3) It becomes clear with this that the length of a generation differs with the ages of every era and Allah knows best. And they agreed, from those whose sayings are accepted, that the last of the Atbā’ al-Tābi’īn lived until the boundaries of 220”

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(1) Correct opinion is that he died at the year 100 after the Hijrah and this is what ibn Ḥajar رحمه الله mentioned in al-Taqrīb under the biography of ‘Āmir bin Wāthilah Abū al-Ṭufayl
(2) i.e he died at 170 or 180
(3) If it is regarded from the year 170 or 180 then 50 years after that which makes it 220 or 230

Benefit: in some authentic narrations the word ثم الذين يلونهم (then those who follow them) has occurred thrice without any doubt from the narrator which means that the followers of the Atbā’ al-Tābi’īn are also included in the Salaf (Like al-Bukhari, al-Tirmidhi, al-Darimi, Ishaq bin Rahuyah, Qutaybah bin Sa’id, Ahmad, al-Shafi’i etc)