Usually none.
Long ago BIOS(which isn't really part of an OS...) was stored on ROM.
These days you've usually got your OS installed on Hard Drive or a SSD drive.
Most computers nowadays do not store any portion of the operating system in ROM. Among those that did and still do, only the kernel and basic system libraries are placed in ROM.
ROM
ROM - the read-only memory
read-only memory
circut board - the read-only memory (ROM)
ROM(read only memory) is the place where the operating system is stored in the computer. == == Ok, it doesn't take Einstein to realise that ROM cannot be updated. So if you want the ability to upgrade an operating system, it can't be on ROM. Also consider disk costs v memory costs. Again, you do not need to be a Nobel Prize winner to figure it out.
It is typically burned into a tiny ROM chip on the phone's circuit board.
BIOS
ROM - Read Only Memory, is a non-volatile section of memory which contains the programs which will start running when the computer is first turned on. These ROM programs could contain the entire operating system, or could start the basic input/output functions which load the operating system in from another location, such as stored on a disk.
The operating system has nothing to do with the ROM chip
This is hard to say precisely. However the Minuteman I and II guidance computers stored their software on read only tracks on a harddisk platter, and the Apollo guidance computer stored its software in core rope ROM. But neither of these actually had an operating system, their software ran directly on the hardware with no intermediate layers.
Ok, it doesn't take Einstein to realise that ROM cannot be updated. So if you want the ability to upgrade an operating system, it can't be on ROM. Also consider disk costs v memory costs. Again, you do not need to be a Nobel Prize winner to figure it out.