Partition maximum heights are dependent on several factors. Stud width, stud type, stud gauge and stud centres. The number of board layers and footprint width also effect the maximum height. All these effect the strength and stability of the system and thus the height it can be built to. Larger studs, heavier stud gauge, reduced stud centres and increased board layers all result in a higher max system height.

Designers often use the ​industry wide guidance of L/240 @200Pa. This limits the maximum height of any partition by defining a maximum permitted lateral deflection at mid height. L is the height of the wall, so no more that L/240 lateral movement at mid height should occur under a 200Pa UDL.

Similarly, BS5234 Part 2 defines duty rating which also limits maximum height based on a loading criterion. In this case a line load of 500N is applied at 1500mm above the base and the maximum lateral deflection is measured. 15mm - 20mm deflection is classed as Medium duty, 10mm - 15mm is Heavy Duty and 10mm or under is Severe duty.

The duty rating classification of a partition covers other factors beyond its lateral stiffness as described above, including impact resistance, crowd loading and pull out resistance for example. 

All of the above relates to the system cold state maxium height. This would be applicable where you are not required to achieve any fire resistance from the system. If you do need the system to provide fire resistance the maximum height (fire state height) may be lower than the cold state due to the effects of temperature and or limits placed by the regulations based on the tested sample height.

For example from the Siniat Partitions Section of the Drywall Manual:

The system above has a maximum height of 5250mm (cold state) but if you need to achieve the stated fire resistance performance the maximum height is limited to 5000mm in this case.