The delocalised nature of hyperconjugation I have always thought I understood hyperconjugation well until recently, in my post on Regioselectivity of bromination of alkenes, I began to question my understanding of this concept. Hyperconjugation is essentially an MO concept which can be generalised to include any sort of intramolcular orbital interaction between one set of occupied molecular or atomic orbitals with another such set of unoccupied orbitals, belonging to adjacent atoms or groups of atoms in a molecule. A most excellent introduction to this concept can be found here. This is not the IUPAC definition, but anyway, the emphasis of my question is not on the definition so there is no point being pedantic here. This term is most commonly evoked to explain the mechanism by which alkyl groups "donate" electron density to stabilise carbocations. 

I am aware that there have already been multiple posts, with good answers, on this concept:


What is hyperconjugation?
Stabilisation of carbocations through hyperconjugation
Inductive effect and hyperconjugation - one elephant, different parts?
Hyperconjugation involving other bonds


In my post which discusses the nucleophilic attack on the cyclic bromonium ion intermediate, I was enlightened by Martin through one of his comments: 


  I am certain there is hyperconjugation, as there already was hyperconjugation in a substituted alkene. There probably is always something to which we refer to as hyperconjugation. You are thinking in localised orbitals, which is only one viewpoint...


Just like he said, my conception of hyperconjugation had always been how Ron frequently describes it as - a localised phenomena. Specifically, in the context of stabilising carbocations, I see it as an interaction between a $\sigma$ bonding MO of the $\ce {C-H}$ or $\ce {C-C}$ bond with the empty p orbital of the carbocation. However, this comment made me think about the delocalised nature of these interactions. MO theory is supposed to be based heavily on delocalised interactions, yet we are considering rather localised interactions here. Well, it is not as localised as a 2-centre 2-electron bond, but still it is a rather localised picture. I would not like to contend this. But... I would just like to pose the following related questions below:

If hyperconjugation should be more seen as a more delocalised phenomena, would distance and geometry play such important factors? Please take note of my examples below and pay attention to them as you attempt a response at my question. 

For example, if I have a tert-butyl group bonded to a carbocationic centre, would there also be (significant enough) hyperconjugative interactions between the $\ce {C-H}$ $\sigma$ bonding MOs with the empty p orbital of the carbon atom. Note that by looking at the more localised picture, such as that given by Ron, we would likely only expect the $\ce {C-C}$ bonds to be significant hyperconjugative donors. Additionally, specifically, in my case of the bromonium ion, would there be significant hyperconjugative interactions between the bonding MOs of the $\ce {C-C}$ and $\ce {C-H}$ bonds of the adjacent alkyl groups with the low-energy $\ce {C-Br}$ $\sigma$* LUMO?

Any help is much appreciated!
I'll try to answer your question through the exemples you give us.
Where are the electrons ?
If you look at the hybridized orbitals making the C-H and the C-C bonds, you can see that the more the bond is polarized, the worse electron donor you have. It's quite understandable since if the bond is polarized, the electron density will be closer to the heteroatom but further to the carbocation that needs stabilization.

Usually the donor ability goes in this order increasingly:
C-F &lt; C-O &lt; C-N &lt; C-H &lt; C-C
Hyperconjugation from C-C to carbocation
Following the &quot;rule&quot; stated before, the stabilization of a carbocation will be best with an adjacent C-C bond. And this is in accordence with what we learn in school since the more alkyl groups nearby, the more stable is the carbacation. Not only because of the increased overall electron density (donor inductive effect) but also because of the hyperconjugation. This is also the base of some reactivity (1,2-C-C bond migration)
Hyperconjugation in the bromonium case
We can easely extend the thing we just saw for the exemple of a bromonium intermediate. In fact it is important to dissociate the cases of the bromonium and the transition state for the bromonium openning.
The bromonium has two bonds with a carbon atom. One could expect the opening reaction to occur in competition between these two sites. We can see that the C-Br bond (Scheme 2, left) can be aligned with a C-C bond, so if we take a look at the molecular orbitals, we will see that this filled sigma C-C bond can interact with the empty C-Br sigma*. Thus creating a destabilization of the C-Br bond (filling a anti-bonding molecular orbital destabilizes the bond) trough an hyperconjugation intercation. But if we look at the second C-Br bond (right) we see that there are no such interaction since there are no filled molecular orbital which can interact with the sigma* of the C-Br bond.

In term of reactivity, the destabilization of the left-hand C-Br bond will favor the breaking of this  bond instead of the other one.