Short and simple: rods control reactor power, and boron adds positive reactivity (due to its burnup) to compensate for fuel use at end of life.
hmm ok so where are you going to put a neutron in a reactor where it will last long enough to decay on it's own? I have never heard of a "magic cup" that can do that. Like I said before the neutron will leak or get absored, they will exist in the reactor only small fractions of a second.
The neutron can go several mean free paths before absorption... or it can be absorbed right away. Let's consider leakage and absorption to be essentially the same beast as far as neutron economy goes. The point is that a neutron can probably exist for any amount of time in the core (within reason). Reactor control has a lot to do with delayed neutron precursors.
And... I'm not sure who brought up multi-group diffusion, but I'll bite. 6 groups is a statistical model... but as far as MCNP goes, isn't everything just a statistical model? I'm not sure if deterministic models work the same way... I've only dealt with MCNP at this point. Any deterministic folks in here?