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The adoption credit is limited to the lower of the actual adoption costs or the maximum credit amount. As a brief example let's suppose that actual costs are $5,000 and the maximum credit is $7,000. You would then be entitled to $5,000.
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I found this at the following:
How Do I Claim the Adoption Tax Credit?
What do I do when the IRS asks for qualifying expenses on line 5?
Because you do not need to document expenses for children with special needs, simply enter $13,170 for 2010 as long as your child receives adoption assistance. [Although 2010 instructions haven't yet been issued, the 2009 IRS instructions related to special needs adoption state: "If you did not claim any adoption credit for the child in a prior year, enter $12,150 on line 5 even if your qualified adoption expenses for the child were less than $12,150 (and even if you did not have any qualified adoption expenses for this child)."]
Is any of this correct?