Tier 1: will give you the ability to heal the host providing some extra time in lane and a nice edge in fights.

Tier 2: will give extra attack speed to the host increasing their damamge. Really nice on heroes like Thrall.

Tier 3: Increases the range on your (Q) allowing you to pick up kills you otherwise might miss.

Tier 4: Your Heroic ability, I prefer taking this so I can Symbiote the monstrosity for extra push and a more global presence.

Tier 5: Extra healing is always a good thing.

Tier 6: Adds a slow effect to your (W) , allowing you and your host to pick up more kills.

Tier 7: Great for end game team fights, you can double your damage and healing.

Your priority targets for Symbiote should be melee warriors like Sonya, Arthas, Tyrael, Muradin.
So far Stitches is my #1 pick if you have a choice. I have found that Uther and Abathur can be a great combo if Uther is played aggressively enough.
A good second choice is melee assassins like Illidan and Zeratul.
A good third choice would be a Hero like Gazlowe.
Finally ranged assassins and supports should be lowest on your priority list.

Keep in mind however this priority list will change with the composition of your team, the objectives of the map, and the current state of the game you are in.

As Abathur you have to have global map awareness, keep an eye on your team but also look for opportunities to push lanes. Remember that you can (Q) lane minions, merc camps and your own Monstrosity, timing this well may allow you to take down towers will the enemy is else where.

If Abathur has chosen to Symbiote you, first remember you are not invincible but you can be more aggressive. Your opponents may lose sight of the fact that you have Abathur's help, if they do it will usually result in a kill.

For melee heroes, don't be afraid to get up close and personal. Abathur's Spike Burst can deal significant damage and with the proper talents it can heal you and slow enemies. Abathur's Stab can also secure kills that may otherwise get away from you so don't be afraid to chase a little bit.

For ranged heroes, you should be the last option for Symbiote but if he chooses you, make sure you aren't too far from the action. If you are too far away, you complete neutralize anything he can do for you and your team.

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