A dispenser assembly designed to tangentially dispense a sheet from a roll of sheet material including sheet material formed from two webs, each web having lines of weakness positioned transversely across the web which allows the web to be separated into a plurality of sheets, the lines of weakness of one web being offset from those of the other web. The dispenser assembly includes (1) a base arranged to hold the roll of sheet material and to couple the dispenser assembly with an environment structure; (2) a first roller and a counter roller between which the sheet material is movable towards a dispensing outlet; and (3) a cradle arranged to support the roll of sheet material and to unwind the sheet material towards the first roller whatever a consumption level of the roll of sheet material. The first roller and the counter roller are positioned relatively to each other spaced according to a fixed nip therebetween to generate a braking force on the sheet material sufficient to break the line of weakness of the web at the dispensing outlet or downstream the dispensing outlet.