The question is about identifying which factor is not essential for the formation of a tropical cyclone. Let's analyze each option to determine which one is not required:

1. Weak winds: For the formation of a tropical cyclone, weak or minimal wind shear is essential. This allows convection to occur and develop vertically, allowing for the structure of the cyclone to remain intact. Therefore, weak winds are crucial.
2. Coriolis force: The Coriolis force is necessary for the rotation of the cyclone. It allows the system to spin and organize itself. The absence of Coriolis force means no cyclone development, which is why tropical cyclones do not form near the equator where this force is minimal. Hence, the Coriolis force is required.
3. Convective instability: This is the condition where warm moist air at the surface rises and cools as it moves upwards, causing further instability. This process is vital in the development and intensification of cyclones as it feeds energy to the system.
4. High precipitation: While tropical cyclones indeed cause heavy precipitation, high precipitation is a result of cyclone formation rather than a requirement for its formation. Precipitation occurs due to the organized convection within the cyclone.

Based on the analysis above, the factor that is not required for the formation of a tropical cyclone is High precipitation. Precipitation is an effect of the cyclone, not a precursor or requirement for its development.