With the recent addition of Zz'rot portal, a handful of people have tried to break it to some extent. I am one of those.

What's / Why Zz'rot? Let's start by looking at what Zz'rot gives.

As of 5.1 , here are the stats of Zz'rot Portal:

50 Armor
50 Magic Resist
+100% Base Health Regen
UNIQUE - POINT RUNNER: Grants +30% bonus movement speed that builds up over 2 seconds when near turrets or Void Gates.
Unique Active: Spawns a Void Gate at target location for 150 seconds. Every 4 seconds the gate creates a volatile Voidspawn that travels down the nearest lane, attacking enemy minions and exploding when attacking structures, but ignoring champions and void targets. 150 second cooldown.
Every additional Voidspawn after the third one gains damage equal to 50% of your armor + 50% of your magic resistance.

The most important about this is the fact that after the third minion spawned, each minion have 50% your armor and MR IN DAMAGE.

Without a doubt, this may seems odd to most as to why I have chosen Annie Hastur for this. (Yes, Hastur truly is her last name ;D )

The reason behind this is Annie's E: Molten Shield. With your shield only, you add 50 damage to your minions.
(With this build and your Molten Shield, you get about 300-380 additional damage.)

With the base damage of the minions to turrets being 50 +20 per champion level, that adds up to over 600 damage per kamikaze minion. Combine this with Tibber's ~100 dps, and your own ad for about another 100 damage and you have there a dead tower in less than 10 seconds. (If placed correctly, your second minion should have the buff since it is not given on creation but rather as soon as the third is spawned.)

Another good reason is that she is *supposed* to be a support, thus has good base damage.

Pros:

A tower falls in about 10 seconds of you going at it.
You are very hard to kill.
Very frequent stuns due to 40% CDR
Tibbers end up on a 48 sec cooldown. (On 45 seconds lifetime for 3 seconds cooldown if not killed.)

Cons:

You don't do THAT much damage to players.
When Tibbers is out, your burst is pretty weak.
Early level, very focused on two character micro'ing.

When engaging your opponent at early levels, you can take advantage of a stalemate fight in which you used Tibbers if they didn't kill him. Annie's link length is long enough that you can be under tower and have Tibbers hit minions in the middle of the lane.

Other nice mechanic about Tibbers is that he will restart his attack animation every time you hit R which can give you a good amount of control over your last hitting through him.

To Note: Killing Tibbers gives 50 gold. That's a Tank Minion worth of gold. Do not over farm with him if you are worried your opponent might get the Tibbers kill easily.

Turret Pushing:

When hitting a turret at early levels, it is most of the time better to have Tibbers tank for the minions rather than the turret hitting the minions as he doesn't do much at early ranks. Later on, it might be worth delaying the time at which he gets hit.

Once you have Zz'rot, you can start taking out turrets without even needing minions. Your AoE damage combined with Tibbers gives you enough clear speed to deny any minions and force your Void Minions to kill the turret. During that time, Tibbers will have to tank the turret. If you have minions, Tibbers might not even need to die for a turret.

Please note that this build would be perfectly acceptable as a support. You get CDR, resist and later on, a way to pressure the map.