I was trying to understand the nutrient uptake in the brain. how does the blood flow regulate it? If it is only limited to BBB, how do neurons which are centrally located get the nutrients?
I am not sure I understand your question correctly. The blood brain barrier per definition separates the blood from the brain, which means the barrier is the collective of every vessel wall from the largest to the smallest capillary. The vessels are in the brain in high densities, but the blood is separated from the neuronal network at all times - in a healthy brain. There are a lot of blood vessels inside the brain, but none can be 'after' the blood brain barrier.
Each neuron or glia cell needs to be close enough to each capillary that it gets enough through diffusion. Both neurons and glia can influence blood vessels to control blood flow by demand.
from your question I gather that you have a different understanding of the blood brain barrier, which might stem from different definitions when we talk about the brain.
If we talk about the brain as an organ, which is enclosed in the skull, then we can say that there are a lot of blood vessels inside the brain. But there is no "between the skull and BBB".
The blood brain barrier is the combined surface/cell/vessel wall of every blood vessel inside the brain. Every blood vessel is part of the blood brain barrier. The blood brain barrier separates the brain - but this case we are talking not about the whole organ, but mean only the combined network of neurons and glia cells - from the blood (enclosed in vessels). Every nutrient and oxygen has to pass through the blood vessel wall (blood brain barrier) to reach the neurons/glia or on the reverse, metabolites have to get back to the kidney/liver to be taken care of.
Maybe another analogy would help visualize it. Our digestive system forms from the mouth through the stomach and intestines to our anus a continuous pipe, if you so will. So the complete surface of our digestive system is still the "outside" of our body, though we carry our food "inside".
In a similar fashion will all the blood never be "inside" the brain - meaning the combined network of the neurons and glia. So the only other option for the neurons to get nutriens after they pass the blood brain barrier is passive diffusion. The diffusion constant of each nutrient will determine the maximum distance 2 capillaries can be away from each other to support the neuronal and glia tissue between them.