As Hero999 points out, a voltage controlled resistor or potentiometer is the most flexible, but a parameter controlled one is much simpler to simulate and is adequate if you only need to set or step its initial value, which is then fixed within each run.
If you need actual potentiometers, here are the models I use:
potentiometer.asy is parameter controlled - set the instance parameter Rtot to total track resistance and wiper to the wiper position (0 to 1). Use a .param or .step param command on your sim for control. e.g to sweep it 0% to 100% in 10% steps :
.step param pot1 0 1 0.1
and on the actual potentiometer instance:
Rtot=10K wiper={pot1}
potentiometerVC is voltage controlled with the wiper position set by a control voltage in the range 0 to 1V, with respect to the circuit universal ground node 0. Simply ground the control voltage source's negative terminal, drop a net label on its positive terminal, and the same net label on the potentiometerVC's control terminal (far end of dotted line opposite wiper). Its total track resistance is set by the instance parameter Rtot.
Both limit the effective wiper position to the range 0.001 to 0.999 as the LTspice SPICE engine cant handle resistances actually going to zero. When the wiper position is zero, its at the bottom end of the track if the symbol hasn't been rotated.