Can you claim a girlfriend's son as a dependent?

If I work full-time, earn $31,000 a year, have no other income and support my girlfriend and her child who both aren't being claimed by the father as dependents. Can I:
a - claim my girlfriend's son as a dependent? (qualifying relative maybe?)
b - file for Head of Household?

I think I am right, but cannot find the answers online.

Actually: http://www.ftb.ca.gov/individuals/hoh/faq.shtml#4
says I can claim the child, but cannot file as HOH. Still... would it be qualifying relative or child?

For anyone who is looking at this in the future, this is from IRS.gov:

"A taxpayer can claim as a qualifying relative a child whose parent (or other person for whom the child is defined as a qualifying child) is not required to file an income tax return and either

* Does not file an income tax return, or
* Files a return only to get a refund

For example, Todd's girlfriend, Eva, and her two children have lived with him in his home for the entire tax year. Eva did not work and had no gross income. She is not required to file an income tax return and will not file. Todd has provided more than half of their support for the entire year. Eva and her two children are Todd's qualifying relatives because the member of household or relationship test, gross income test, and support tests were all met.

Consider the same facts in the example, except Eva had wages of $2,000 and income taxes were withheld from her wages. She is not required to file a return and only files to get a refund of the income taxes withheld. Eva does not file a claim for the earned income tax credit or any other credits or deductions. She and her children are Todd's qualifying relatives if the relationship or member of household, gross income, and support tests are all met. "

In the span of 12 minutes you asked and answered your own question - I think that's gotta be some kind of record! And your answer was absolutely spot on. You primarily need to pay attention to meeting the various tests: relationship (or member of hh), gross income, and support.

short answer... no