League-of-legends – Is Rylai’s slow affected if I use Tiamat as well

Rylai's is a decent pick on Vladimir, but ever since his nerf from his passive on the conversion of HP into AP I don't take it anymore and just focus on pure AP item like Rabadon's Deathcap.

But to answer the question, all of Vladimir's spells would proc Rylai's Unique ability, UNIQUE: Your spell damage slows the target's movement speed by 35% for 1.5 seconds (15% for multi-target spells and damage-over-time spells).

Which means, your transfusion would slow the target by 35% but the rest of your abilities since they are all AoE, multi-targeting spells, would only slow by 15%.

You mustn't mix up life steal and spell vamp.

Life steal steals on physical damage (meaning auto-attack for vlad). In fights, you very rarely use your auto-attacks to deal big damage because you're a caster.

Spell vamp steals on magical damage (meaning all of his spells), this is want you want if your plan is to steal more life.

• Zhonya's Hourglass is great because vlad's ult has low range but must be cast in battle engage to hit the most enemies and for the 15% extra magical damage. The two second invulnerability will allow you to stay alive in the heart of the battle if you get targeted.
• I also very often use Hextech Revolver with Vlad, but you need some AP. It's no use having 50% Spell vamp if you don't deal any damage.

Vlad spells cost life, the good thing about more spell vamp is you can get your life back faster with transfusions minion lines and you can cast life costing spells (specially Tides of Blood that stacks) with less impact on your life.

EDIT : I went to have a quick look at all the different Vlad builds. All (or nearly all) of the descent builds have hextech revolver in them with its evolution to will of the ancients - give more AP, more spell vamp and an aura :-)