3 situations: different pre-boil gravity?

Will there be a difference in pre-boil gravity in these situations (in theory and practice):

1) I mash with the *exact* amount of water needed to hit my pre-boil volume on the mark. For instance, 3qts of water/lb grain. No sparge. Lauter slowly to boil kettle to get 7gallons pre-boil.

2) I mash with the same amount of water as above (3qts/lb), but this time, I fly sparge while it's lautering. Lauter slowly (same rate as sparge) to boil kettle to get 7gallons pre-boil. [I assume that the sparge water will push the mash wort down, so that only mash wort moves into BK, and all sparge water stays in MLT. Is this correct?]

3) I mash with less water, say 1-2 qts. Fly sparge. Lauter (slowly) to boil kettle to get 7gallons pre-boil. [In this case, "sparge water" will end up in the BK. Though that sparge water should have rinsed the grains of remaining sugars]

I'm trying to get a better idea of mashing/lautering in regards to water volume. Thanks for any help!

In theory (and probably in practice, though are ways to mess up a fly sparge), you'll get the best efficiency with method (3) and the worst efficiency with method (1). The logic of sparging is relatively simple. You've got a sopping pile of grain with a significant amount of dissolved sugar, and you want to get the sugar out. Fly sparging will rinse the grains a bit more thoroughly.

At the same time, don't forget that grain is cheap.