When a Karmapa dies, his rebirth is recognized again by his closest students, most often by Shamarpa, the second-highest lama in the Karma Kagyu lineage.
When the 16th Karmapa passed away in 1981, centuries-old Tibetan politics, Chinese geo-political interests in the Himalayas, and old-fashioned greed conspired to make the recognition of the 17th Karmapa a little more difficult than usual.