Shireen Baratheon targets a character with Head of a Dwarf attached. Assuming the target's controller has no other character with Head of a Dwarf attached, what happens if he would claim or move power to his house?

1. He must place it on the target, but cannot. Nothing happens.
2. Placing the power on the character with Infamy does not involve the character claiming power, so the power goes to the target.

Relevant card and rules text:

Shireen Baratheon

Any Phase: kneel Shireen Baratheon to choose a character. Until the end of the phase, that character cannot claim power.

Head of a Dwarf

Attached character gains infamy. If attached character's controller would claim power for his or her House, that power must be placed on a character with at least one Head of a Dwarf card attached.

Infamy

When you claim power or move power to your House, you may place it on any card with the “Infamy” keyword instead of placing it on your House.

Khudzlin said:

I would say that your solution #2 is correct.

The most important thing here is the wording of Infamy. Note that the character is not claiming power.

Since using Infamy to put the power on the character is not the character claiming power, Shireen's ability does not affect them at all.

Correct - the only time a character claims power is through Renown and through card effects that specifically state that the character claims power.
Infamy is not claiming power, it's "placement" of power on a character like described above.

I think some of the specific text used when power is put on a character is "character claims power", "place power on character", and "put power on character" where Renown is defined as claiming power.

Since the Brotherhood agenda uses the same wording ("you must place that power on a Brotherhood character"), I take it Shireen doesn't stop that, either.