The fuel line linking is critical.
Basically what it does is let you drop off dead weight as early as possible. Weight is drag and costs fuel, so you want to get rid of empty tanks and engines as soon as possible.
I
sometimes have experimented with the outermost engine-bottomed stacks having further fuel-tanks (not in connected stacks, but in sliced 'rings') hanging off from radial decouplers and fuel-linked to to the ring above and the ring above (and the ring above...) and then into the outermost stack. For an assembly that would not have been able to make the most of full-throttle anyway (for aforementioned air-resistance reasons) putting this additional weight on that slows it down is not a disadvantage if I can still full-throttle (or nearly so) the whole stack but be using the stack rings (from bottom to top) in turn, and keeping everything else topped up longer.
Drop the bottom-most ring when empty, the next bottom-most ring when
that's empty, etc. By then I've sometimes found myself in orbit[1] with almost
all 'engine-bottomed tanks' still full, giving me a good burn off to whatever off-Kerbin trajectory I care to try.
As a (basic) segment-slice diagram, the following is the general plan...
,--centre
|
v
A
3=4=5=H=5=4=3
4 5 H 5 4
2=4 5 H 5 4=2
4 5 H 5 4
1=4-5-H-5-4=1
^ ^ ^ ^ ^
A (capsule)
H <- Centre stack
^ (engine)
1, 2, 3, 4, 5 fuel tanks jetissoned off 1st..5th
= <- decoupler
- <- strut (for strength, these being radial ones but you also need ones that link circumeferencially)
Fuel-transfers (also the probably necessary SASes/etc) not shown, but are 1->2->3->4->5->H, with 4->5 and 5->H being from the bottom tank of the source to the top fuel-tank of the destination (not sure if necessary, but I've always done that, by habit).
Because of the 6-symmetry (or 8-symmetry, of traditional-thickness tanks immediately surrounding the larger sized central core), the 'stages' and fuel-links between (say) the 4-stage and the 5-stage would be via 4a, 4b, 4c... opposing pairs, to be disposed of in turn, as you might imagine, once those sectors of this current 'outer-layer' are a depleted force (this needs to be reflected in the "fuel only" rings, also, either in how you feed or how you jettison). And if you suffer undue wobbles after a part-layer separation event (the circumference strutting between now absent outer sectors and the the (still) adjacent tanks in that 'ring' having gone), you may need to also add struts between the not-first-to-go segment stack and diagonally inwards to an inner-layer to add rigidity/non-elasticity to the structure. (Sometimes I've managed to fit "miss one" links between non-adjacent segments either side of the segments that would be first to go, but it depends on how the rest of the structure aligns. However, if it attaches the terminator to the next ring in, instead, then just repeat in the other direction and you get the diagonally inwards links as just described, for much the same effect.)
(Due to the sometimes highly-fragile nature of the ship, though, I tend to shut off engines, decouple then start the engines up again (powering out of the debris once I can see it's not likely to spin into an engine), for some non-atmospheric 'stagings'.)
I don't think it's as good a method as having
all jettisonable fuel-stacks 'work for their supper' with their very own engines[2], arranged in layers so that you shuck off 'rings' of boosters[3] (or the simpler "asparagus" model just talked about, which sounds similar but I've not seen/tried during my rather lonesome endeavours), but if/when an economic model states that engines are at a premium while mere fuel tanks are much cheaper it
could be a more cost-effective way to lift.
[1] With a judicious lateral component to the upward flight. Although I've
also experimented with "just go up!", right from my first experiments with KSP, with only solar orbits (and unclosed, solar-escape orbits) to aim for once I've gotten beyond the Mun.
[2] Also, I've had rather wide designs that sometimes do (but sometimes don't) clip the launch structure, creating imbalances either straight away or as soon as that sector of inner-rings runs out of fuel early..
[3] And, within that ring, symmetrically opposite pairs of boosters in turn, if I've edited the .craft file to get what was laid down as sixfold/eightfold symmetries to now behave as similarly aligned triplets/tetruplets of two-fold symmetric addons, for the fine control.