In a report, the analysts claim that Samsung will maintain the leading status over the next few years, with its shipments to increase to 560 million units in 2019. This is a 114 percent boost from 2015..

The company does have the advantage that its biggest customer is Samsung Electronics which just happens to make most of the world's smartphones.  It is expecting demand to grow from 239 million units in 2016 to 290 million units in 2019, the report said.

Samsung's number one rival, Apple is expected to initially adopt AMOLED panels for iPhones to be launched in 2017, using Samsung Display's supply. This will see more than 40 million units in 2017, 80 million units in 2018 and 120 million units in 2019.

Chinese smartphone vendors, including Vivo, Oppo, GiONEE, Huawei and Lenovo, have adopted or moving to AMOLED and Samsung Display's combined shipments to them will increase from 99 million units in 2016 to 150 million units in 2019.

Japan Display, Sharp, China- and Taiwan-based panel makers are expected to start making AMOLED panels and Samsung Display may begin to face competition in 2019 or 2020.