It's actually mostly designed by ARM holdings. Apple simply designs the SoC layout and chooses the components.

The GPU is a design from Imagination Technologies, the CPU is an Apple design. What part of the SoC is "mostly designed by ARM"?

The CPU. Apple licenses ARM's reference designs, then creates an SoC around that.

The last SoC where this has been the case is the A5 (using the the ARM Cortex-A9 MP). The Apple A6 and A7 don't use ARM cores and neither does Qualcomm in their Snapdragon SoCs.

ARM just comes up with the instruction set. The cores are still designed by Samsung, Qualcomm, NVidia, etc.