Kernel memory allocators (see following slides) allocate physical pages, and kernel allocated memory cannot be swapped out, so no fault handling required for kernel memory
Most kernel memory allocation functions also return a kernel virtual address to be used within the kernel space
Kernel memory low-level allocator manages pages. This is the finest granularity (usually 4kB, architecture dependent)
However, the kernel memory management handles smaller memory allocations through its allocator (see slabs / SLUB allocator – used by kmalloc)