Which Windows process is responsible for determining the low level space management and allocation?
For example, that the data goes to this block, this segment etc.
There doesn't seem to be a dedicated file system management process, so I'm pretty sure it's being managed by the Kernel, so it would be the either the "System" process or something hidden managed by the System process. As the file system needs to be managed before the first service boots up, it should be deep in the systems core. (but them again, I don't know the MS source code)
Dedicated Filesystem Management processes would be those for defragmentation.
Any 'process' can access the disks via the Windows API if they have permission.
Where the data ends up on the disk (blocks, segments etc.) is determined by the mass storage drivers (which are (usually) kernel-level) and by the drives themselves.