Infinite, or at least it goes up to whatever cap there is in the software. Sion with 6 Warmog's Armors and a really long game farming Enrage can have an uncapped amount of hp.
if you aren't relying on that farm than i would say 6 Warmog's Armors Cho'Gath with full Feast and a Lulu's Wild Growth
don't ask me how much that is but think, it is 6000 ( Warmog's Armor) plus Cho'Gath's base hp at level 18 (1880) and 6 feast (150 x 6: 900) and Lulu (600) would make it AT LEAST 9380 not including AP on Lulu, runes/masteries, and any shield from other champions
I saw a video of 2 lunetics stacking Veigar and Nasus in custom 1v1 ARAM they played something like 8 hours or maybe even more... Those things are really infinite.
don't ask me how much that is but think, it is 6000 (