The market integration of hybrid off-shore projects, consisting of wind farms and transmission assets connecting different market zones, requires re-examining bidding zone definitions. Policy makers consider separate off-shore bidding zones to optimally integrate off-shore wind farms in power systems. In this paper, we apply Advanced Hybrid Coupling to include off-shore DC transmission lines in flow-based market coupling, and compare different bidding zone configurations. We find that off-shore bidding zones lead to a transfer of welfare: the producers' surplus of off-shore wind farm owners decreases as a result of a lower average price and the congestion rent for TSOs increases. Despite that an off-shore bidding zone signals transmission scarcity better, it impacts the need for support instruments for off-shore wind farms.@en