Unwinder for rolls (B) of paper web material comprising: - a support frame; - a spindle cylinder , rotationally associated with said support frame, capable of supporting a parent roll (B) having a longitudinal axis (x); - unwinding means acting by contact with said parent roll (B) to unwind from it a web (N) of paper material; - actuator means capable of keeping said unwinding means in contact with said parent roll (B); - a command and control unit (C), characterized in that it comprises: - first motor means (M1) capable of applying a rotation movement to said spindle cylinder ; - two support and drive rollers for said roll (B), provided with respective longitudinal axes (y, y'), arranged symmetrically with respect to a vertical plane (π) passing through said longitudinal axis (x) of the parent roll (B); - measurement means to measure the instantaneous radius of said parent roll (B); - measurement means to measure the rotation speed of said spindle cylinder ; - measurement means to measure the quantity of web (N) unrolled from said parent roll (B) by unit of time; - measurement means to measure the weight unloaded from said parent roll (B) onto said two support and drive rollers ; - second motor means (M2), associated with said two support and drive rollers , capable of giving them a synchronous rotation movement around their respective axis (y, y'); - third motor means (M3) associated with said actuator means and capable of moving said spindle cylinder vertically, wherein said command and control unit (C) is capable of receiving and processing the values detected by said measurement means to command said first (M1), second (M2) and third (M3) motor means, so as to maintain constant the weight force unloaded onto said support and drive rollers from said roll (B) as the diameter of the latter varies. - a support frame; - a spindle cylinder , rotationally associated with said support frame, capable of supporting a parent roll (B) having a longitudinal axis (x); - unwinding means acting by contact with said parent roll (B) to unwind from it a web (N) of paper material; - actuator means capable of keeping said unwinding means in contact with said parent roll (B); - a command and control unit (C), characterized in that it comprises: - first motor means (M1) capable of applying a rotation movement to said spindle cylinder ; - two support and drive rollers for said roll (B), provided with respective longitudinal axes (y, y'), arranged symmetrically with respect to a vertical plane (π) passing through said longitudinal axis (x) of the parent roll (B); - measurement means to measure the instantaneous radius of said parent roll (B); - measurement means to measure the rotation speed of said spindle cylinder ; - measurement means to measure the quantity of web (N) unrolled from said parent roll (B) by unit of time; - measurement means to measure the weight unloaded from said parent roll (B) onto said two support and drive rollers ; - second motor means (M2), associated with said two support and drive rollers , capable of giving them a synchronous rotation movement around their respective axis (y, y'); - third motor means (M3) associated with said actuator means and capable of moving said spindle cylinder vertically, <EOS>