Two pathways for gas accretion based on the requirement that pebble heating must cease for gas accretion to commence. (1) The pebble isolation pathway: the protoplanet reaches M_iso and the pebbles are trapped at the outer edge of the gap. (2) The pebble decay pathway: the pebble flux decays due to radial drift. If the protoplanet previously attained sufficient mass, its envelope contracts by radiative heat loss, resulting in gas accretion. The core mass distinguishes giant planets formed by the two pathways.