As the title states, I'm wondering whether or not a Medium titan fighter can wield a Huge bastard sword.
Rules-as-written states you can wield a weapon one size category larger by staging it up and adding a penalty. For example, a light weapon becomes 1-handed, a 1-handed weapon becomes 2-handed, and 2-handed weapons are impossible.
With the feat Exotic Weapon Proficiency (bastard sword), you can treat the bastard sword as a 1-handed martial weapon. That said, if you have that feat could you, in theory. wield it two-handed if it were bigger than your own size?
If you can, you could—once again, in theory—with the feat Exotic Weapon Proficiency (bastard sword) also wield a Huge bastard sword as a 2-handed Large weapon, which is what a titan fighter is built to wield.
If this is allowable, what would the penalty on attack rolls be for wielding such an awesome blade?