tom's basically right as far as he goes...
Whether FADEC or hydromechanical control, there are a few things the engine requires:
1) At any given instant, there's a maximum fuel flow limit the engine can stand. This is determined by an acceleration flow schedule. It's determined by pressure (usually compressor discharge pressure), temperature (usually at the HP compressor inlet), and RPM. If this limit is exceeded, a stall or surge or too-rich blowout of the burner is likely.
2) Also at any given instant, there's a minimum limit, to prevent too-lean blowout (flameout) of the combustor.
3) Fuel flow to hold constant RPM lies somewhere in between 1) & 2). A governor (linked to the throttle/thrust lever) trims fuel flow until RPM stabilizes at the desired speed. This is one point on the "steady-state line".
When the throttle advances, the governor senses an underspeed, calls for more petrol, and fuel flow rises until it reaches 1). As RPM reaches the new demand point, the governor backs off fuel to re-stabilize RPM. This is a new point on the "steady-state line".
During a decel, fuel flow can only drop to the min. limit in 2).
"Smart" controls like FADEC can impose other limits as well - like turbine temperature or pressure ratio.
Airflow control is another whole different matter - generally it's not directly linked to the throttle, though.