We do not know the exact number of the population who remained in their former homeland after Prince Árpád set out to retake the Carpathian basin in the 9th century. If we start from the data given by the Hungarian chronicles, it is almost certain that only one-tenth of the Hungarian speaking populace left the Caucasus region to resettle in the Carpathian basin. Likewise, during the Huns 375 AD European campaign only a selected number of fighting force set out to conquer Europe. Most probably, those Hungarian tribes that left behind remained scattered at several places in the vast area between the Black Sea and the Caspian Sea region where they established their own independent states. One of such states we know of established by the Sabirs in the Transcaucasian region, but near the Meotis swamps might have also existed a second Hungarian state.
One of the first medieval records about the eastern Hungarian state came from the Cumans that established a state in the early middle ages at present day Moldavia. The Cumans informed Dominican monks, who visited their region to convert them to Christianity, about an existing eastern Hungarian state in the Caucasus ruled by the Árpád Dynasty.
Sometime, in the late 1220s, Dominican monk Otto following the information obtained from the Cumans set out to meet eastern Hungarians in the Caucasus region and convert them to Christianity. Otto successfully reached the east coast of the Black Sea and made contact with the Hungarian tribes that lived in the region in an organized state.
In the 14th century a papal bull also mentions the existence of an eastern Hungarian state in the Caucasus. The document was issued in 1329, and it indicated that there was a region near the Black Sea that was called Hungary and ruled by the Árpád Dynasty. At that time, the name of the ruler was "Jeretán" or "Gyeretyán". Unfortunately, the papal bull doesn't say the exact location of the Hungarian state, but it is possible that it was located at present day Georgia. The existence of the Árpád Dynasty in the Caucasus confirmed by the papal bull indicates that the House of Árpád died out on the male side in 1301 only in the Carpathian Basin, but in the Caucasus the descendants of Attila and Árpád continued to rule vast areas.
(alfahir.hu – translated by hungarianambiance.com)