From the website of the Salafi preacher Salman al-Oadah
Some people on Internet came up with the reference “Tafsîr Ibn `Abbâs”. Did Ibn `Abbas write any commentary of the Qur’ân known as “Tafsîr Ibn `Abbâs”?
Answered by Sheikh Muhammad al-Qannâs
It is well known that `Alî b. Abî Talhah had a copy of the commentary of Ibn `Abbâs which was praised by the scholars for being the best in its attribution of authenticity to Ibn `Abbâs.
Ahmad b. Hanbal said: “There is a manuscript in Egypt of Qur’ânic commentary related by `Alî b. Abî Talhah. If a man were to travel there solely for its purpose, it would not be a major hardship.”
Ibn Hajar al-`Asqalânî writes: “This copy was in the possession of Abû Sâlih, the scribe of al-Layth. It is narrated from Mu’âwiyah b. Sâlih through `Alî b. Abî Talhah through Ibn `Abbâs. Al-Bukhârî has it by way of Abî Sâlih. He (al-Bukhârî) uses it a lot in his Sahîh in what he related from Ibn `Abbâs.”
Al-Suyûtî writes: “The commentary of the Qur’ân that is attributed to Ibn `Abbâs is too considerable to count, coming in various narrations by various means of transmission. One of the good lines of transmission from him is that coming by way of`Alî b. Abî Talhah.”