An apparatus for connecting rig lines (48, 58) of a managed pressure drilling system on a floating rig to a riser, the rig lines (48, 58) including a rig flow line (48a, 58a) for conducting flow of the MPD system and including a rig control line for conducting control (48b, 58b) of the MPD system, the riser having an internal passage, the apparatus comprising: a riser manifold disposed on the riser and having a first face (102, 200) comprising: a first mechanical connector disposed on the first face (102, 200), a first flow coupling for conducting the flow of the MPD system, and a first mating plate (120, 130, 210, 220) disposed on the first face (102, 200), the first mating plate (120, 130, 210, 220) having a first control coupling (122, 124, 132, 212, 224) for conducting the control of the MPD system; and a rig manifold configured to removably position adjacent the riser manifold and having a second face (152, 200), the rig manifold comprising: a second mechanical connector disposed on the second face (152, 200), a second flow coupling disposed on the second face (152, 200) and disposed in fluid communication with the rig flow line (48a, 58a) for conducting the flow of the MPD system, and a second mating plate (170, 180, 210, 220) disposed on the second face (152, 200), the second mating plate (170, 180, 210, 220) having a second control coupling (172, 174, 182, 212, 224) disposed in control communication with the rig control line (48b, 58b) for conducting the control of the MPD system, the first and second mechanical connectors (106, 156) configured to mechanically connect together, the second flow coupling configured to mate in a flow connection with the first flow coupling for conducting the flow of the MPD system, at least one of the first and second mating plates (120/170, 130/180, 210, 220) being adjustable relative to the respective first and second face (102, 152, 200), the second control coupling (172, 174, 182, 212, 224) configured to mate adjustably in a control connection with the first control coupling (122, 124, 132, 212, 224) for conducting the control of the MPD system. a riser manifold disposed on the riser and having a first face (102, 200) comprising: a first mechanical connector disposed on the first face (102, 200), a first flow coupling for conducting the flow of the MPD system, and a first mating plate (120, 130, 210, 220) disposed on the first face (102, 200), the first mating plate (120, 130, 210, 220) having a first control coupling (122, 124, 132, 212, 224) for conducting the control of the MPD system; and a rig manifold configured to removably position adjacent the riser manifold and having a second face (152, 200), the rig manifold comprising: a second mechanical connector disposed on the second face (152, 200), a second flow coupling disposed on the second face (152, 200) and disposed in fluid communication with the rig flow line (48a, 58a) for conducting the flow of the MPD system, and a second mating plate (170, 180, 210, 220) disposed on the second face (152, 200), the second mating plate (170, 180, 210, 220) having a second control coupling (172, 174, 182, 212, 224) disposed in control communication with the rig control line (48b, 58b) for conducting the control of the MPD system, the first and second mechanical connectors (106, 156) configured to mechanically connect together, the second flow coupling configured to mate in a flow connection with the first flow coupling for conducting the flow of the MPD system, at least one of the first and second mating plates (120/170, 130/180, 210, 220) being adjustable relative to the respective first and second face (102, 152, 200), the second control coupling (172, 174, 182, 212, 224) configured to mate adjustably in a control connection with the first control coupling (122, 124, 132, 212, 224) for conducting the control of the MPD system.