Does the kernel keep track of where a process starts in memory or does the CPU?

I'm trying to implement paging in a simple kernel I'm writing. I understand page directories and page tables and how to map memory from a virtual address to a physical address. I've implemented these concepts in my kernel already. The part I don't understand is if the kernel should keep track of where each program starts in memory (by a page offset) or if the CPU handles this. If the CPU handles it is this what a TSS is for? Thanks.