A method for selectively feeding rolls of paper coming out of a log saw unit (10), wherein the log saw unit (10) comprises (n) feeding channels (12) for feeding logs (11) towards a cutting device (13) provided at the outlet with (n) unloading belts (14) in a number equal to the feeding channels (12), comprises a step of generating a stop signal relating to a portion of a packaging unit downstream of the log saw unit (10) further to the detection of accumulation of rolls (11′) and/or of stopping of a packaging machine, as well as a step of attributing said stop signal to a feeding channel/sub-group of feeding channels (12) operatively associated with the portion of the packaging unit, called “feeding channels/sub-groups of feeding channels (12) subject to stopping”, wherein the method—upon receipt of the stop signal—comprises at least the steps of: ending the cutting of the log (11) in progress on all of the (n) feeding channels (12) of the log saw unit (10), selectively stopping the forward movement of a new log (11) towards the cutting device (13) just in the feeding channels/sub-groups of feeding channels (12) subject to stopping through the stopping of the forward movement of the carriers (15) of the carrier device (16) of the feeding channels/sub-groups of feeding channels (12) subject to stopping, proceeding without interruption in the operative feeding channels (12), namely those not subject to the stop signal, with the cutting of the logs (11) in succession.