the invention provides a drilling system for drilling subsea wells from a floating mobile offshore drilling unit , the system comprising a subsea bop . the system is distinctive in that the subsea bop has relative small weight and size , the system includes no marine riser but the system comprises : flexible choke and kill lines arranged between the subsea bop and the modu , means for drill string guidance and cleaning , for guiding when inserting or taking out a drill string from the bop and for drill string cleaning when pulling the drill string out from the bop , means for controlled leakage of seawater into a recovery funnel arranged below the means for drill string cleaning but above the bop , and means for return from the recovery funnel to the modu of drilling fluid and seawater leaked into the recovery funnel .