Simple question about CPUs and processes

[security at revolutionsp.com]

Hi list,

I'd like some insight on the following; Me and a friend were discussing
tech stuff and he said that, when using dual (or more) CPU systems, it is
the hardware itself (and alone) choosing which CPU will execute this or
that process.

But I think it is the OS kernel (FreeBSD in this case) and the SMP
implementation that decide this process should live in CPU0 or CPU1, ie
it's FreeBSD itself choosing on what CPU a process will reside in.

I'm by no means an experienced programmer, so I can't check this for
myself; just following logic and intuition, I think it makes sense it is
the OS keeping track of what process is in which CPU. Which approach is
right? Please add as many technical details as needed.