Pickup, an ability that allows your Pokémon to randomly pick up an item has got a new twist to it, first is a list of all Pokémon with the ability:

Anyway, in Pokémon Emerald, Pick-Up is determined by level aswell adding an added element for those who dont both raising their Zigzagoon. Below is a list of the items you can get (hover over the pictures for the name...especially for TMs):

Lv. Common Uncommon V. Unc. Rare V. Rare
1 - 10 Potion Antidote Super Potion Great Ball Repel Escape Rope X Attack Full Heal Ultra Ball Hyper Potion Nugget
11 - 20 Antidote Super Potion Great Ball Repel Escape Rope X Attack Full Heal Ultra Ball Hyper Potion Nugget King's Rock
21 - 30 Super Potion Great Ball Repel Escape Rope X Attack Full Heal Ultra Ball Hyper Potion Rare Candy King's Rock Full Restore
31 - 40 Great Ball Repel Escape Rope X Attack Full Heal Ultra Ball Hyper Potion Rare Candy Protein Full Restore Ether
41 - 50 Repel Escape Rope X Attack Full Heal Ultra Ball Hyper Potion Rare Candy Protein Revive Ether White Herb
51 - 60 Escape Rope X Attack Full Heal Ultra Ball Hyper Potion Rare Candy Protein Revive HP Up White Herb TM 44 - Rest
61 - 70 X Attack Full Heal Ultra Ball Hyper Potion Rare Candy Protein Revive HP Up Full Restore TM 44 - Rest Elixer
71 - 80 Full Heal Ultra Ball Hyper Potion Rare Candy Protein Revive HP Up Full Restore Max Revive Elixer TM 01 - Focus Punch
81 - 90 Ultra Ball Hyper Potion Rare Candy Protein Revive HP Up Full Restore Max Revive PP Up TM 01 - Focus Punch Leftovers
91 - 100 Hyper Potion Rare Candy Protein Revive HP Up Full Restore Max Revive PP Up Max Elixer Leftovers TM 26 - Earthquake