Inspired by Does Death's Shadow grow when blocking a creature while the player is taking damage?
Let's say I control a Phyrexian Dreadnought - a 12/12 Trampler. My opponent is on 12 life and has a Death's Shadow, currently 1/1.
I attack, opponent blocks. Trample says I need to assign "lethal damage" to the blocker, presumably 1 damage in this case, and then any excess damage goes to the player. But if I assign 1 damage to the Death's Shadow and 11 damage to the player, then the Death's Shadow becomes a 12/12 with 1 damage marked on it, which is not lethal. In fact, some math shows that I need to assign at least seven damage to the Death's Shadow to actually kill it, in which case opponent only takes 5 trample damage.
Can I trample over for 11, or only for 5?