Tsong-kha-pa died in 1417 and is said to have been transfigured and carried up into heaven while predicting to a great crowd the future glories of his church. His mortal remains, however, preserved in a magnificent mausoleum within the Gandan monastery, still receive great veneration.

Among his more eminent disciples were Byams-chen-chos-rje and mKhas-grub-rje who in Tibetan art are often represented as accompanying him. The first played a considerable part in China. The Emperor Yung-Lo sent an embassy to invite Tsong-kha-pa to his capital. Tsong-kha-pa felt unable to go himself but sent his pupil to represent him. Byams-chen-chos-rje was received with great honour[949]. The main object of the Ming Emperors was to obtain political influence in Tibet through the Lamas but in return the Lamas gained considerable prestige. The Kanjur was printed in China (1410) and Byams-chen-chos-rje and his disciples were recognized as prelates of the whole Buddhist Church within the Empire. He returned to Tibet laden with presents and titles and founded the monastery of Serra in 1417. Afterwards he went back to China and died there at the age of eighty-four.

mKhas-grub-rje founded the monastery of Tashilhunpo and became its abbot, being accepted as an incarnation of the Buddha Amitâbha. He was eighth in the series of incarnations, which henceforth were localized at Tashilhunpo, but the first is said to have been Subhûti, a disciple of Gotama, and the second Mañjuśrîkirti, king of the country of Śambhala[950].

The abbot of Tashilhunpo became the second personage in the ecclesiastical and political hierarchy. The head of it was the prelate commonly known as the Grand Lama and resident at Lhasa. Geden-dub[951], the nephew of Tsong-kha-pa, is reckoned by common consent as the first Grand Lama (though he seems not to have borne the title) and the first incarnation of Avalokita as head of the Tibetan Church[952]. The Emperor Ch'êng Hua (1365-1488) who had occasion to fight on the borders of Tibet confirmed the position of these two sees as superior to the eight previously recognized and gave the occupants a patent and seal. From this time they bore the title of rGyal-po or king.

It was about this time that the theory of successive incarnations[953] which is characteristic of Lamaism was developed and defined. At least two ideas are combined in it. The first is that divine persons appear in human form. This is common in Asia from India to Japan, especially among the peoples who have accepted some form of Hindu religion. The second is that in a school, sect or church there is real continuity of life. In the unreformed sects of Tibet this was accomplished by the simple principle of heredity so that celibacy, though undeniably correct, seemed to snap the thread. But it was reunited by the theory that a great teacher is reborn in the successive occupants of his chair. Thus the historian Târanâtha is supposed to be reborn in the hierarchs of Urga. But frequently the hereditary soul is identified with a Buddha or Bodhisattva, as in the great incarnations of Lhasa and Tashilhunpo. This dogma has obvious advantages. It imparts to a Lamaist see a dignity which the papacy cannot rival but it is to the advantage of the Curia rather than of the Pope for the incarnate deity of necessity succeeds to his high office as an infant, is in the hands of regents and not unfrequently dies when about twenty years of age. These incarnations are not confined to the great sees of Tibet. The heads of most large monasteries in Mongolia claim to be living Buddhas and even in Peking there are said to be six.

The second Grand Lama[954] enjoyed a long reign, and set the hierarchy in good order, for he distinguished strictly clerical posts, filled by incarnations, from administrative posts. He was summoned to Peking by the Emperor, but declined to go and the somewhat imperative embassy sent to invite him was roughly handled. His successor, the third Grand Lama bSod-nams[955], although less noticed by historians than the fifth, perhaps did more solid work for the holy see of Lhasa than any other of his line for he obtained, or at least received, the allegiance of the Mongols who since the time of Khubilai had woefully backslidden from the true faith.

As mentioned above, the conversion of the Mongols to Buddhism took place when their capital was at Peking and chiefly affected those resident in China. But when the Yüan dynasty had been dethroned and the Mongols, driven back into their wilds, were frequently at war with China, they soon relapsed into their original superstitions. About 1570 Altan[956] Khagan, the powerful chief of the Tümed, became more nearly acquainted with Tibet, since some Lamas captured in a border fray had been taken to his Court. After causing China much loss and trouble he made an advantageous peace and probably formed the idea (which the Manchus subsequently proved to be reasonable) that if the Mongols were stronger they might repeat the conquests of Khubilai. The Ming dynasty was clearly decadent and these mysterious priests of Tibet appeared to be on the upward grade[957]. They might help him both to become the undisputed chief of all the Mongol tribes and also to reconquer Peking. So he sent an embassy to invite the Grand Lama's presence, and when it was not successful he followed it with a second.

The Grand Lama then accepted and set out on his travels with great pomp. According to the story he appeared to the astonished Mongols in the guise of Avalokita with four arms (of which two remained folded on his breast) and the imprint of his horse's hoofs showed the six mystic syllables om mani padme hum. These wonders are so easily explicable that they may be historical.

A great congregation was held near Lake Kokonor and Sanang Setsen records an interesting speech made there by one of his ancestors respecting the relations of Church and State, which he compared with the sun and moon. The Lama bestowed on the Khagan high sounding titles and received himself the epithet Dalai or Talai, the Mongol word for sea, signifying metaphorically vast extent and profundity[958]. This is the origin of the name Dalai Lama by which the Tibetan pontiff is commonly known to Europeans. The hierarchy was divided into four classes parallel to the four ranks of Mongol nobles: the use of meat was restricted and the custom of killing men and horses at funerals forbidden. The observance of Buddhist festivals was made compulsory and native idols were destroyed, but the deities which they represented were probably identified with others in the new pantheon. The Grand Lama specially recommended to the Mongols the worship of the Blue Mahâkâla, a six armed representation of Śiva standing on a figure of Ganeśa, and he left with them a priest who was esteemed an incarnation of Mañjuśrî, and for whom a temple and monastery were built in Kuku-khoto.