An apparatus for connecting rig lines of a managed pressure drilling (MPD) system on a floating rig to a riser , the rig lines including a rig flow line for conducting flow of the MPD system and including a rig control line for conducting control 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 comprising: a first mechanical connector disposed on the first face , a first flow coupling for conducting the flow of the MPD system , and a first mating plate disposed on the first face , the first mating plate having a first control coupling 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 , the rig manifold comprising: a second mechanical connector disposed on the second face , a second flow coupling disposed on the second face and disposed in fluid communication with the rig flow line for conducting the flow of the MPD system, and a second mating plate disposed on the second face , the second mating plate having a second control coupling disposed in control communication with the rig control line for conducting the control of the MPD system , the first and second mechanical connectors 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 , the second control coupling configured to mate adjustably in a control connection with the first control coupling for conducting the control of the MPD system . a riser manifold disposed on the riser and having a first face comprising: a first mechanical connector disposed on the first face , a first flow coupling for conducting the flow of the MPD system , and a first mating plate disposed on the first face , the first mating plate having a first control coupling 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 , the rig manifold comprising: a second mechanical connector disposed on the second face , a second flow coupling disposed on the second face and disposed in fluid communication with the rig flow line for conducting the flow of the MPD system, and a second mating plate disposed on the second face , the second mating plate having a second control coupling disposed in control communication with the rig control line for conducting the control of the MPD system , the first and second mechanical connectors 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 , the second control coupling configured to mate adjustably in a control connection with the first control coupling for conducting the control of the MPD system . <EOS>