Several clinical treatments, including extracorporeal membrane oxygenation (ECMO), haemodialysis and antibiotic therapy, require fluid transport to patients through a tubing system consisting of several tubes joined by various connectors. Thrombotic complications can arise within these connectors when the tubing system is used to transport blood. Indeed, the junction between the tubes and the connectors can introduce geometric discontinuities that can cause flow separation. These features promote flow-induced thrombosis, necessitating the administration of anticoagulants such as heparin and thrombin inhibitors, which significantly increases the risk of bleeding in patients. For these reasons, optimising the design of tubing connectors to reduce thrombogenesis is crucial to improving patient health and comfort. To this end, we perform direct numerical simulations (DNS) of blood flow through connectors used in extracorporeal medical devices and estimate clot formation within the device through the model developed by Yang et al., which accounts for the deposition and growth of the thrombus. Multiple connector configurations are considered, allowing for a systematic investigation of the effect of geometrical details of the connector on the thrombus formation and evolution. Particular attention is paid to flow characteristics associated with thrombogenesis, such as flow separation regions and vortical structures. By correlating these haemodynamic features with predicted thrombus growth, we assess the thrombogenic potential of each geometry and identify design characteristics that minimise clot formation. Based on these results, we will then provide guidelines for improving connector design with the aim of reducing thrombogenicity in devices used for extracorporeal circulation.