I don't know offhand, but I know enough to pull the Form 8889 instructions: https://www.irs.gov/pub/irs-pdf/i8889.pdf

Look at lines 3 and 6, it appears the straightforward answer is "no":  "When figuring the amount to enter online 3, apply the following rules.

But my parents can not pay for my medical expenses out of their HSA account, so shouldn't I be able to open my own HSA since I am not a dependent but am covered under a family HDHP?  The Publication you sited does not exclude me from opening an HSA on my own I was covered by a HDHP I am not a dependent, I do not have any other insurance and I am not a spouse. I need to find somethings that strictly excludes me from this tax benefit.  Also I would not be splitting the contribution I would be contributing to my HSA at the family rate.

Groan, I think AnswerXChange lost my first answer when I logged in, sorry if you see this twice.  I think you are eligible to fund your own HSA due to HDHP coverage, but I don't see any way you can fund it to the family limit, only the individual limit. Not sure of course, I suggest you just start googling around and reading the rules for yourself.

If the individual has family HDHP coverage, he can contribute to his HSA up to the family limit.  See page 4 of this IRS reference:  <a rel="nofollow" target="_blank" href="https://www.irs.gov/pub/irs-pdf/p969.pdf">https://www.irs.gov/pub/irs-pdf/p969.pdf</a>