DisplaySearch expects the AMOLED market to reach $11.3 billion in 2013, up 60% from 2012 ($6.9 billion). The market is still dominate by a single supplier (Samsung Display) and a single customer (Samsung), and it's still too early to tell whether OLEDs can really become a mainstream market.
DisplaySearch also released the interesting chart above that shows price comparison between AMOLED and LCD (a-Si and LTPS) panels. Most of the growth in 2013 will come from the 4.99" Full-HD (441 PPI) panel used by the GS4, and DisplaySearch estimates that 52 million of these panels will be produced in 2013 (over $3.2 billion in revenues).
Interestingly, DisplaySearch says that Samsung indeed considered using an LCD for the GS4, but in the end they obviously managed to produce those high-density display. Currently it's not clear what kind of display will be used in the Note 3, but DisplaySearch expects it to adopt an OLED panel.