It depends on the ability but basic attacks should increase.
Edge-to-edge calculations are used for basic attack ranges on all champions. Skillshot particles are created from the center of your champion and aren't affected by size increases (unless otherwise specified) so skillshots are basically center-to-edge targetting. Targeted abilities used to all be calculated center-to-center but Riot has been trying to move them towards matching basic attacks and being edge-to-edge.
In Cassiopeia's latest rework her E was changed to an edge-to-edge targeting but there were so many complaints from players who had to re-learn the range in addition to everything else that changed about her that it was moved back to a center-to-center system. If they had kept it edge-to-edge then size increases would increase her range but now it is center-to-center again so size increases do not benefit her.