I have income from self employment and my partnership. Can I associate either with my heath care premiums? Income from my partnership is much smaller than my self employm

Yes, you can take a deduction for self-employed health insurance while using the Marketplace. Please see this answer from HelenaC.

If you are self-employed, click on Where do I enter my health insurance premiums if I'm self-employed?

If you are self-employed and if you paid your ObamaCare health insurance premiums (Form 1095-A) with after-tax dollars, TurboTax will take the deduction after you enter your 1095-A Health Insurance Marketplace Statement.

• In TurboTax, under the Health Insurance tab, choose We all had health insurance coverage all year.
• Answer Yes that you were enrolled in a plan from HealthCare.gov.
• Choose Obamacare plan (1095-A).
• Enter your form.
• After you enter your 1095-A form, on the Do any of these situations apply? screen, choose Self-employed and bought a Marketplace plan.

Thank you. I understand I can associate my health care premiums with my self employment. Can I associate my health care premiums with my partnership, if my partnership income is vastly less then my self employment income? I prefer to associate it with my partnership.

To clarify, I have both self employment and a partnership. Both seem to be options to associate my health insurance premiums with. In the turbotax section where entering in 1095A, I have to choose which of the two (self employment or partnership) to associate the premiums with. Can I pick either? Do I have to pick the one with the significantly larger income? 

You can associate it with either one.  You do not have to pick the one with the higher income.  However, do remember, it is only deductible to it takes your income to $0.  It cannot create a loss for you.