Deep convective systems are ubiquitous over the tropical oceans and are central to the Earth radiation budget due to their upper-level cloud shields. Possible evolution of the morphology of these cloud shields with climate change remain poorly understood. In this study, the sensitivity of the cloud shield to environmental conditions is therefore investigated using a large dataset of atmopsheric profiles from renalaysis and satellite observations. The initial environmental conditions in stability, thermodynamics, and dynamics are explored. Multilinear regression between morphology and environment is used in a 2D phase space linked to the life cycle of the systems, namely the time to reach the maximum extension and the associated maximum area. Dynamical drivers show stronger morphological control than the thermodynamic factors. The result reveals an overwhelming role for wind shear over a deep tropospheric layer in explaining the scale dependence of cloud shield morphology. In particular, the variability of the shield growth rate is very well explained by deep layer shear (R2>0.8). The depth of the systems is also strongly related to dynamics and secondly to water vapor loading. These results feed the debate on the relative role of deep- vs. low-level shear in influencing deep convection and extend previous precipitation-centric considerations to the cloud shield of the systems. Possible underlying mechanisms are discussed, and the need to extend previous theoretical considerations on idealised convective geometry towards the whole spectrum of deep convective systems populating the tropical oceans is emphasised.