Apple's custom processor designs are interesting products. Apple moved from single to dual core processors for the iPhone 4S in 2011 and since then, Apple's newer smartphone and tablet models have introduced increasingly more and more powerful processors. Apple have designed a custom ARM core and switched to a 64-bit architecture a year sooner than those manufacturers supplying components for Android manufacturers. Indeed, following the logic through enough and Apple's early advance into 64-bit processors is the reason why several of the established mobile processor manufacturers are using ARM's reference processor core designs rather than their own custom core, such as Qualcomm and Nvidia with the Snapdragon 810 and Tegra X1 respectively. Apple's dual core processors perform admirably whilst sipping at power; unfortunately, Apple to not licence or sell on their processors so we cannot see how well they might perform with Android software.
The next generation Apple system on chip designs, the Apple A9 and A9X (designations for the iPhone and iPad models respectively) are believed to be built on a 14nm or 16nm process. Industry experts have been considering and debating the likely manufacturer for the next generation Apple processor between two protagonists, Samsung or TSMC (Taiwan Semiconductor Manufacturing Corporation). Some analysts believe that TSMC will get the lion's share of the new Apple chipset because they have superior manufacturing abilities, whereas others are more confident in Samsung's new 14nm FinFET chipset manufacturing process. However, the smaller the processor die, the better the likely benefits to the device but the harder the manufacturing process is. The situation is unclear but it appears that both Samsung and TSMC are experiencing "yield difficulties" with the newer generation, smaller processors. By "yield difficulties," this means that the processors are proving difficult (and therefore expensive) to manufacture to the necessary quality. Perhaps because of the difficulties manufacturers are experiencing producing small die size processors in sufficient quantities, we've seen a consensus forming in the industry: neither Samsung nor TSMC will gain exclusive rights over the chipset. Apple will instead divide up the manufacturing load, although opinions vary as to the divide between the two companies.
We've also seen stories linking Qualcomm with Samsung because of Qualcomm's processor issues. Qualcomm use TSMC as a manufacturing partner for the Snapdragon 810 processor, which according to unnamed sources is having "bigger & broader" overheating issues. These overheating issues appear to be encouraging Qualcomm into moving to smaller die sized processors, so as to remain competitive. It's unclear the time horizon for this, especially if Samsung are suffering from yield issues at their smaller die manufacturing plant.