Having held several MLPs for many years, I can give you my experience, but others will need to speak to the IRS code that affect the answer to your questions.
I assume your talking about common units of a Master Limited Partnership (MLP)
I have never received a 1099DIV for MLP distributions. These should come to you on the MLPs K-1 that should be sent directly to you and not through your brokerage....at least that's how I get mine.
The K-1 will have boxes 1 through 20 showing various sources of income the MLP must pass through to you, the limited partner. Most tax preparation software, such as TurboTax, will have you input these numbers off the K-1 into TT and for many you can even do an auto download from the MLP website to TT. Your 'capital account' in the MLP is recalculated each year in box L of the K-1. However, this is not your tax basis which is determined in the year you sell some or all of your MLP units by adding back the cumulative Sec. 1245 depreciation and subtracting past cumulative losses (if any). The distributions you receive are, by definition, return of capital and are not reported on your tax return. Any earnings will be in box 1 and reported on your form 1040 as ordinary income. Any loss is accumulated and used when you sell some/all units.
MLPs are very complicated for tax purposes.There's a guy named 'Reel Ken' who posts at Seeking Alpha that has written some of the better descriptions on the taxation of MLPs.