How the Christian Canon Developed

Remember we are dealing with the concept of 'New Testament canon' rather than 'gospels.' I can't account for the origins of the Gospel of the Hebrews or any other text that might have circulated OUTSIDE of a New Testament canon. All that I can say for certain now, with regards to the organization of the cane was that in the beginning ...

Evangelium + Apostolikon

No explicit identification of author and then in the third century Alexandria the gospel is identified as 'according to Mark.'

The explicit identification of Mark as the author of the Evangelium was prompted by Polycarp and the process is witnessed by the Letter to Theodore. The canon of Polycarp (established circa. mid second century) had:

Evangelium according to John (also called Mark?) + Acts + Apostolikon (Pauline, deutero-Pauline, Johannine, 1 Peter other texts + Revelations?)

I am fairly certain that Polycarp's text was mis-identified as 'the Diatessaron' and formed the basis to the canon of Ephraim. Ephraim's canon was the same as the canon of the author appropriated by Tertullian to make Against Marcion Books Four and Five.

Then at the time of Irenaeus the familiar canon that we now know:

the Gospel in four (Matthew, Mark, Luke and John) plus the rest that followed.

The EXACT shape of the collection might have been slightly modified (in terms of the order of the Pauline epistles especially) and the exclusion of certain writings. But the collection already took a familiar shape by the time of Irenaeus.