The Apostles accepted Paul as an Apostle (Galatians 2:9), but they compiled their gospels separately from the letters of Paul, since why would they base their accounts on someone who wasn't an eyewitness?
Mark
A letter (70-255 AD) from Clement of Alexandria on how Mark wrote his gospel:
"As for Mark, then, during Peter's stay in Rome he wrote an account of the Lord's doings, not, however, declaring all of them, nor yet hinting at the secret ones, but selecting what he thought most useful for increasing the faith of those who were being instructed. But when Peter died a martyr, Mark came over to Alexandria, bringing both his own notes and those of Peter, from which he transferred to his former book the things suitable to whatever makes for progress toward knowledge. Thus he composed a more spiritual Gospel for the use of those who were being perfected. Nevertheless, he yet did not divulge the things not to be uttered, nor did he write down the hierophantic teaching of the Lord, but to the stories already written he added yet others and, moreover, brought in certain sayings of which he knew the interpretation would, as a mystagogue, lead the hearers into the innermost sanctuary of that truth hidden by seven veils. Thus, in sum, he prepared matters, neither grudgingly nor incautiously, in my opinion, and, dying, he left his composition to the church in 1, verso Alexandria, where it even yet is most carefully guarded, being read only to those who are being initiated into the great mysteries." http://earlychristianwritings.com/text/secretmark.html
Secret Mark was ignored after heretics stole it and wrote heresies into it.
Luke
Muratorian fragment, the earliest known list of the canon, 170 AD, on Luke's gospel:
"
The third book of the Gospel is that according to Luke. Luke, the well-known physician, after the ascension of Christ, when Paul had taken with him as one zealous for the law, composed it in his own name, according to [the general] belief. Yet he himself had not seen the Lord in the flesh; and therefore, as he was able to ascertain events, so indeed he begins to tell the story from the birth of John." http://www.bible-researcher.com/muratorian.html
Information on the gospel of Luke,
Gospel of Luke:
"The oldest manuscript with the start of the gospel, Papyrus Bodmer XIV (ca. 200 CE), proclaims that it is the
euangelion kata Loukan, the Gospel according to Luke. This attestation probably does not stem from reading Irenaeus (
Adv. haer. 3.1.1) or Tertullian (
Adv. Marcionem 4.2.2), nor Clement of Alexandria (
Paedagogus 2.1.15 and
Stromata 5.12.82), who also ascribe the third Gospel to one called Luke. Indeed, considering that the immediate recipient of Luke is mentioned in the preface, and given that the author of the third Gospel is aware that many other accounts have been drawn up before him, it is entirely probable that the author had indicated his name on the autograph. (The "most excellent Theophilus" mentioned in the preface of Luke is most likely his patron, as seen in the similar references to "most excellent X" in the prefaces to the
De libris propriis liber of Galenus, the
De antiquis oratoribus of Dionysius Halicarnassensis, the
Scriptor De Divinatione of Melampus, the
Peri ton kata antipatheian kai sumpatheian of Nepualius, and both
Josephi vita and
Contra Apionem of Josephus.) This Luke has traditionally been identified as the one named in Philemon 24 as a co-worker of Paul."
John
Muratorian fragment again, this time on how John wrote his gospel:
"
The fourth of the Gospels is that of John, [one] of the disciples. To his fellow disciples and bishops, who had been urging him [to write], he said, 'Fast with me from today to three days, and what will be revealed to each one let us tell it to one another.' In the same night it was revealed to Andrew, [one] of the apostles, that John should write down all things in his own name while all of them should review it. And so, though various elements may be taught in the individual books of the Gospels, nevertheless this makes no difference to the faith of believers, since by the one sovereign Spirit all things have been declared in all [the Gospels]: concerning the nativity, concerning the passion, concerning the resurrection, concerning life with his disciples, and concerning his twofold coming; the first in lowliness when he was despised, which has taken place, the second glorious in royal power, which is still in the future. What marvel is it then, if John so consistently mentions these particular points also in his Epistles, saying about himself, 'What we have seen with our eyes and heard with our ears and our hands have handled, these things we have written to you? For in this way he professes [himself] to be not only an eye-witness and hearer, but also a writer of all the marvelous deeds of the Lord, in their order."
Paul on Paul:
"I want you to know, brothers, that the gospel I preached is not something that man made up. I did not receive it from any man, nor was I taught it; rather, I received it by revelation from Jesus Christ." (Galatians 1:11-12)
So it would seem that Paul and the gospel writers didn't need to depend on each other for their accounts.
