I am not sure what you mean by "Buddhist-style" meditation but I do not think it was accurate for the Desert Fathers, although some artificial similarities will always exist among ascetic groups, like meditating on scriptures or praying silently. The Christian practice that appears to have been rooted in Indian religious practices is called hesychasm, but the link is hard to prove. You can read Kallistos Ware's intro to the work in Kallistos Ware, Act out of Stillness: The Influence of Fourteenth-Century Hesychasm on Byzantine and Slav Civilization ed. Daniel J. Sahas. Toronto: The Hellenic Canadian Association of Constantinople and the Thessalonikean Society of Metro Toronto, 1995. With regard to what happened to the Desert Fathers and their spirituality, that is a long answer. The Desert Fathers eventually created communities that developed and handed on religious and spiritual practices and ideas that eventually became monasticism. An introductory work to this development can be found in Peter King's Western Monasticism: A History of the Monastic Movement in the Latin Church. (Kalamazoo, MI: Cisterscian Studies, 1999). Monasticism will develop different in the western and eastern churches but the spiritual of the Desert Fathers was carried to Europe through several agents, like John Cassian, whose Institutes helped to promote monastic and ascetic practices in early medieval Europe. Eventually, these practices were transformed by the arrival of new forms of monastic thinking in the 11th and 12th centuries in Europe (affective spirituality) and by the rise of hesychasm and related practices in the east. (See David N. Bell, Many Mansions: An Introduction to the Development and Diversity of Medieval Theology (Kalamazoo, MI: Cistercian Publications, 2000). In that sense, the spirituality and practices of the Desert Fathers persists in modern monastic practices, although transformed by two millennia of development. There are a number of books about the Desert Fathers, but you might try the recent one by William Harmless Desert Christians: An Introduction to the Literature of Early Monasticism. (Oxford University Press, 2004). I don't know if that gives you some idea but if you could tell me what view as a Buddhist practice, I might be able to give a more direct response.