PS2 classics are live on the PS4! And the stand outs of the group has to be the PS2 era Grand Theft Auto trilogy which includes GTA III, Vice City and San Andreas. The download sizes for the 3 games are
GTA III: 1.597GB
GTA Vice City: 2.939GB
GTA San Andreas: 3.211GB
These three games along with others can be downloaded right now for $14.99/£11.99 each. With streaming options, trophies, and upscaled visuals included in the PS4 versions of these PS2 classics.