The item is similar to My Little Unicorn, with faster recharge time at the cost of being unable to damage enemies while under its effects.
If another active item is picked up while in the invulnerability state granted by Unicorn Stump, Isaac will return to normal immediately, becoming able to shoot tears and take damage.
Synergies
4.5 Volt: With some damage source while this item is active, it can be permanently invulnerable inside the room while you have enemies.
???'s Only Friend: The fly can still be controlled while invincible.
Book of Virtues: Spawns an orbital rainbow wisp on the middle ring. Wisps do not deal contact damage and will not take contact damage. When Isaac is invulnerable, wisps become much more vibrant and deal contact damage equal to 2x Isaac's damage -5. If Isaac has less than 2.5 damage, the wisps will deal no damage even if Unicorn Stump is active.
Car Battery: Doubles the duration of invulnerability.
Mom's Knife: Does contact damage in the same direction it was being held at the time of using the Unicorn Stump, giving a massive amount of free damage by ramming into an enemy.
Works the same with the Yes Mother? transformation's knife.
On contact items (Aries, The Virus, etc.): Freely usable in basically every room.
The Ludovico Technique: The tear stays in place while Isaac is invincible; although Isaac cannot move the tear, it will continue to damage enemies during his invincibility. This is very useful for stationary enemies.
Marked: Isaac's tears will still fire, but he will be unable to move the crosshair while invincible.
Blood Donation Machines and 
Devil Beggars.
My Little Unicorn, with faster recharge time at the cost of being unable to damage enemies while under its effects.
If another active item is picked up while in the invulnerability state granted by Unicorn Stump, Isaac will return to normal immediately, becoming able to shoot tears and take damage.
4.5 Volt: With some damage source while this item is active, it can be permanently invulnerable inside the room while you have enemies.
???'s Only Friend: The fly can still be controlled while invincible.
Book of Virtues: Spawns an orbital rainbow wisp on the middle ring. Wisps do not deal contact damage and will not take contact damage. When Isaac is invulnerable, wisps become much more vibrant and deal contact damage equal to 2x Isaac's damage -5. If Isaac has less than 2.5 damage, the wisps will deal no damage even if Unicorn Stump is active.
Car Battery: Doubles the duration of invulnerability.
Mom's Knife: Does contact damage in the same direction it was being held at the time of using the Unicorn Stump, giving a massive amount of free damage by ramming into an enemy.
Yes Mother? transformation's knife.
Aries, 
The Virus, etc.): Freely usable in basically every room.
Cube of Meat, 
Sacrificial Dagger, etc.): The orbital can be used freely in every single room, making it a great alternative source of damage.
The Ludovico Technique: The tear stays in place while Isaac is invincible; although Isaac cannot move the tear, it will continue to damage enemies during his invincibility. This is very useful for stationary enemies.
Marked: Isaac's tears will still fire, but he will be unable to move the crosshair while invincible.
3DS The icon of Unicorn Stump as seen on the lower 3DS screen
The Binding of Isaac: Rebirth
