Empty the side tanks first

Pipe the side boosters into the core so they keep it full while every engine burns, and drop them empty with the core untouched: asparagus staging.

Every engine on a ship drinks from all the tanks it can reach. Left alone, a core with boosters on decouplers drains everything together, so the boosters fall away still holding fuel and the core has spent its own. A fuel line from each side tank into the core changes that: the side tanks keep filling the core, so they empty first, and the side engines no longer drink from the core at all.

Before you start

A core stack (tank and engine) with a side tank and engine on each flank, hung on radial decouplers or on beams. Mirror one side to get the other.

Tap one side tank and then Fuel line on its panel.
Tap the core tank. A line runs from the side tank into the core, arrow pointing inward, and the mirrored side tank gets its own line into the core in the same tap. See Draw a fuel line.
Stage it. Put all three engines in the first stage and the two side decouplers in the stage after. See Staging.

What you should see

At liftoff every engine burns. The core engine draws on the core tank, and the side tanks fill it straight back up, so the core stays full while the side tanks drain. When the side tanks run dry their engines go quiet: fire the next stage to drop them, and the core flies on with a full tank.

Note

A decoupler carries fuel both ways, but a line drawn beside it decides the direction: with the side tanks piped into the core, the side engines can only reach their own tanks. They never drink the core, even after their tanks are empty.

More than one ring

For two rings of boosters, pipe the outer tanks into the inner ones and the inner ones into the core. The fuel moves inward one ring at a time: the outer ring empties first, then the inner one, and the core last.