If Ulamog is entering the battlefield directly from exile, it will see itself when determining which card has the greatest mana value among cards in exile. If that's Ulamog, which seems likely, it will enter with ten +1/+1 counters on it.

Ulamog, the Defiler's first ability will resolve before Ulamog does. If Ulamog is countered or otherwise leaves the stack in response to its triggered ability, the triggered ability will still resolve as normal.

Use the number of +1/+1 counters on Ulamog at the time its annihilator ability resolves to determine how many permanents defending player should sacrifice.

Annihilator abilities trigger and resolve during the declare attackers step. The defending player sacrifices the required number of permanents of their choice before they declare blockers. Any creatures sacrificed this way won't be able to block.

If a creature with annihilator is attacking a planeswalker, and the defending player chooses to sacrifice that planeswalker, the attacking creature continues to attack. It may be blocked. If it isn't blocked, it simply won't deal combat damage to anything.

Ulamog, the Defiler has received a minor update to clarify that the target of the first ability exiles the top half of their library. Its updated Oracle text appears above.