No, Paul didn't have Fed-Ex at his disposal. But here's a great quote from a commendable source:"The circulation of a document began either from the place (or church province) of its origin, whether the author wrote it, or from the place to which it was addressed (if it was a genuine letter — formal epistles would be like other New Testament writings). Copies of the original would be made for use in neighboring churches. The circulation of a book would be like the ripples of a stone cast into a pond, spreading out in all directions at once. When a book was shared by repeated copying throughout a whole diocese or metropolitan area, the close ties between dioceses would carry it from one district to another, where the process would be repeated. From the moment the Christian church required the use of sacred books in addition to the Septuagint [the Greek translation of the OT], i.e., from the time that the worship service incorporated the reading and exposition of lessons taken not only from the Old Testament but also from other writings which were regarded as holy scripture, the number of New Testament manuscripts began to multiply. Thus the letters of Paul would naturally have been read first in the churches he founded, and then become a regular part of the sequence of liturgical lessons. This must have been the situation from the mid-second century, with the founding of each new church requiring the production of another New Testament manuscript."
From: Kurt Aland and Barbara Aland, The Text of the New Testament (Grand Rapids: Eerdmans, 1989), 55.