40nm, 28nm, 16nm,...

Most companies in the ARM market are fabless. This means they design the SoCs but manufacturing is outsourced to so-called foundries.
There are only few companies on the market which are able produce modern SoCs. Nearly all ARM processors are made by TSMC, Samsung or GlobalFoundries.

While older and cheap SoCs are still made in 40nm process, most current ones use 28nm.

For modern A57,A72 cores you need a 16nm process.
This process was started by TSMC in mid 2015. In the beginning, Apple used major part of production for its A9 SoCs. Starting 2016, other big companies use this process, too. E.g. Qualcomm has designed its Snapdragon 820 chip for the 16nm process.

It will take a while until small companies like Allwinner and Rockchip will have access to 16nm process and will be able to produce high end SoCs. In the meantime, they will design mid range products using matured 28nm process.

There were rumours that Apple will be again customer for the next step. There should be a 10nm process sometimes mid 2016. But Apple seems to still use 16nm process for the A10 Fusion chip found in iPhone7 introduced in September 2016.