Tier 1: Karthus, Anivia, Ryze, Morgana, Orianna, Cassiopeia, , Vladimir, Swain, Kennen.
Tier 2: Twisted Fate , Ahri, Gragas, Veigar, Kassadin, Rumble, Diana, Katarina, Zyra, Mordekaiser, Galio.
Tier 3: Lux, Fizz, Viktor, Zilean, Ezreal, Malzahar, Tristana, Kog'maw, LeBlanc, Xerath.
Tier 4: Fiddlesticks, Sion, Ziggs, Akali, Lulu, Syndra, Brand, Heimerdinger.
Top 5 AP Carries:
Karthus - What can I say? Probably the best AP carry in the game right now, he can farm so easily, good mana sustain with his E, his wall of pain covers pretty much the whole lane, great slow as well magic resist reduction, great for any team comp. No need to roam when you can sit at mid and farm while getting kills and assists for other lanes. When dead, can still cast abilities for a few seconds, making him great for cleaning up fights. Even after the nerfs to the wall of pain, he is still very viable.
Ryze - Ryze - Ryze is quite a unique form of AP/Mana carry because he can get damage out of building mana instead of ability power. This is very useful since many of the mana items provide great defensive stats, making him very tanky and useful in lategame teamfights. His damage is great, burst or DPS, amazing passive which allows his overload to have close to no cooldown. Great spell vamp which can make him a very sustained champion in teamfights.
Morgana - Morgana is almost always banned in ranked games and for a good reason. Her snare is insanely overpowered, lasting 3 seconds when maxed. Very good lane sustain with passive, magic resist reduction from her pool which also helps her farm a lot of minions. Her black shield can be used on the carry to not get cc'ed at all, and last of all, her overpowered ult. Combined with zhonyas, this can bring a ton of AoE damage in teamfights and stun the entire enemy team while taking no damage.
Cassiopeia - Cassiopeia has been known as one of the more difficult champions to master, but when done so she is a monster. Her noxious blast provides great utility, poke, farming and zoning. She has unmatched DPS except for possibly karthus with her 0.5 second cooldown twin fang, as well as vision with her miasma. Her ultimate takes a bit of skill to master but when it is mastered it can deal tons of damage to the enemy team and stun them if timed correctly. Cassiopeia can take down jungle camps fast, as well as dragon and baron with her DPS.
Orianna- With the new buffs to Orianna, she is now returned to competitive play and is now a very viable pick in ranked games. She is quite a hard champion to counter and her AoE burst damage and offers a ton of utility with her crowd control, shield and movement speed boost.
Questionable picks:
Brand - The main reason I rank Brand as tier 4 is his bad scalings and lack of mobility. For example, compare Brand to Morgana. They both have an AoE ability, skillshot cc ability and a multitarget ult.
Dark Binding > Sear
3 seconds > 2 seconds
300 base > 240 base
0.9 AP > 0.65 AP
Dark Binding also has a longer range.
Tormented Soil > Pillar of Flame
Magic Resist Reduction > No magic resist reduction
425 base > 255 base
1.0 AP > 0.65 AP
Tormented Soil and Pillar of flame have the same mana cost.
Morgana offers more utility with her shield, when put on a carry they are not able to be crowd controlled for 5 seconds.
Soul Shackles > Pyroclasm
The main reason for soul shackles being a much better ability than pyroclasm is that it has a stun. Soul Shackles will also deal more damage in teamfights as it can hit all 5 team members while pyroclasm is ****.
Cheers for checking my tier list out, please let me know if I am missing anyone 
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