Cleave

Cleave causes a melee hero's attacks to deal a portion of their damage in a radius in front of them. Ranged units cannot cleave.

Mechanics
If a unit has cleave, its attacks deal damage in a circular area infront of it on each attack (or in the case of Kunkka, on one attack whenever it is off cooldown). Only melee heroes can cleave, attacks with projectiles can never cleave. The primary attack target is not hit by the cleave damage. The attack has to actually hit the target in order to cleave. A missed attack, be it caused by evasion or a blind effect, does not cleave.

Damage

The damage is entirely based on the attacking unit's attack damage. It does not matter how much damage the attacked unit actually took as cleave only checks the damage value of the attacking unit. The damage is not reduced by armor value. Only the armor type and damage block reduce it. Cleave damage is always physical, so it never affects units in ethereal state, and always pierces spell immunity.

Radius

A cleave's effect radius is shaped like a circle. This circle is infront of the attacking unit, so that the attacking unit is always at the edge of the circle. This means that cleaves reach always twice as long as their tooltips say, since the value in the tooltips always tells the radius of the circle.

Stacking

Cleave is an attack modifier which fully stacks with any other modifier. It does not interfere with any attack modifier. This means that for example the armor reducing effect of Desolator is still only applied to the primary attack target. However, if an attack modifier increases or reduces damage, the modifier will affect the cleave damage, even when the modification is not visible in the damage value in the hud.

Attack damage modifying effects which are not shown in the hud include all critical strikes and. These do affect the damage of cleaves.

The damage from is the only added attack damage which can be cleaved. All other sources of added attack damage (like with all bashes) are not cleaved.

Cleave Stacking

Cleave also fully stacks with other sources of cleave. Each source of cleave works fully independent. Their damage is not summed up, each of them deal their own instance of damage.

As an example, with level 4, buffed with a level 4  and 2 Battle Furies will deal 4 instances of damage on each attack to units within 200 range infront of him, 2 damage instances to units within 200-250 range and 1 instance to units within 250-300 range. This is because in this scenario, one source has a radius of 200, 2 of them have 250 radius and one has 300 radius, so all 4 hit units within 200 range, but only one of them hits units up to 300 range away. In this scenario, units within 200 radius take 185% damage from cleave, units between 200-250 range take 135% damage and units between 250-300 take 65% damage.

Sources of Cleave

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Splash
Splash is basically the ranged version of Cleave. It works in a similar way as cleave, does, with the difference being that the damage is dealt in a radius around the attacked unit. The primary target is not hit, but the damage type can vary. If the attack misses, no splash damage is applied in the area, or in case of Elder Dragon Form, 50% of the damage is applied in the area. Splash works with attack modifier the same way as cleave does.

Unlike cleaves, however, splash damage which is physical is reduced by armor value, armor type and damage block. Magical splash damage is reduced by magic resistance and does not pierce spell immunity.

Usually, splash has multiple area of effects, each dealing a different percentage of the attacking unit's attack damage, making units closer to the primary target take more damage than units further away.

Sources of Splash

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