the present invention provides drilling systems for drilling subsea wellbores . the drilling system includes a tubing that passes through a sea bottom wellhead and carries a drill bit . a drilling fluid system continuously supplies drilling fluid into the tubing , which discharges at the drill bit bottom and returns to the wellhead through an annulus between the tubing and the wellbore carrying the drill cuttings . a fluid return line extending from the wellhead equipment to the drilling vessel transports the returning fluid to the surface . in a riserless arrangement , the return fluid line is separate and spaced apart from the tubing . in a system using a riser , the return fluid line may be the riser or a separate line carried by the riser . the tubing may be coiled tubing with a drilling motor in the bottom hole assembly driving the drill bit . a suction pump coupled to the annulus is used to control the bottom hole pressure during drilling operations , making it possible to use heavier drilling muds and drill to greater depths than would be possible without the suction pump . an optional delivery system continuously injects a flowable material , whose fluid density is less than the density of the drilling fluid , into the returning fluid at one or more suitable locations the rate of such lighter material can be controlled to provide supplementary regulation of the pressure . various pressure , temperature , flow rate and kick sensors included in the drilling system provide signals to a controller that controls the suction pump , the surface mud pump , a number of flow control devices , and the optional delivery system .