Apparatus and method for controlling pressure in a borehole

There is described a technique for drilling and controlling the fluid pressure of a borehole (2, 102) during drilling of the borehole. In embodiments of the invention, drill pipe (5) may be arranged in said borehole, the pipe being configured to provide drilling fluid in the borehole. Sealing means (14, 18, 114, 118) may be provided and arranged to sealingly abut an outer surface of the drill pipe to separate said drilling fluid in the borehole on a first side of the sealing means from a column of fluid on a second side of the sealing means. Furthermore, a subsea pump arrangement (12, 112) may be arranged under a sea surface where it receives a flow of said drilling fluid from the borehole. The pump arrangement can operate to pump drilling fluid out of the pump arrangement, and generate a fluid pressure in said drilling fluid at a location upstream of the pump arrangement, said generated pressure being less than or equal to the hydrostatic pressure of said column of fluid on said second side of the sealing means.