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.