Context : Jets are dynamic , impulsive , well-collimated plasma events that develop at many different scales and in different layers of the solar atmosphere . Aims : Jets are believed to be induced by magnetic reconnection , a process central to many astrophysical phenomena . Within the solar atmosphere , jet-like events develop in many different environments , e.g. , in the vicinity of active regions as well as in coronal holes , and at various scales , from small photospheric spicules to large coronal jets . In all these events , signatures of helical structure and/or twisting/rotating motions are regularly observed . The present study aims to establish that a single model can generally reproduce the observed properties of these jet-like events . Methods : In this study , using our state-of-the-art numerical solver ARMS , we present a parametric study of a numerical tridimensional magnetohydrodynamic ( MHD ) model of solar jet-like events . Within the MHD paradigm , we study the impact of varying the atmospheric plasma \beta on the generation and properties of solar-like jets . Results : The parametric study validates our model of jets for plasma \beta ranging from 10 ^ { -3 } to 1 , typical of the different layers and magnetic environments of the solar atmosphere . Our model of jets can robustly explain the generation of helical solar jet-like events at various \beta \leq 1 . This study introduces the new result that the plasma \beta modifies the morphology of the helical jet , explaining the different observed shapes of jets at different scales and in different layers of the solar atmosphere . Conclusions : Our results allow us to understand the energisation , triggering , and driving processes of jet-like events . Our model allows us to make predictions of the impulsiveness and energetics of jets as determined by the surrounding environment , as well as the morphological properties of the resulting jets .