Assume an AGI of 200K. Will a long term capital gain of 700K be subject to a 20% tax rate? Or will the first 300K or so be taxed at 15%, and the rest at 25%? Thank you.

It depends on your filing status.  While capital gains may be taxed at a different rate (including 0%), they are still included in your adjusted gross income, or AGI, and thus can affect your tax bracket.

• Long-term gains are treated much better. Long-term gains are taxed at 15% or 20% except for taxpayers in the 10% or 15% bracket. For low-bracket taxpayers, the long-term capital gains rate is 0%. There are exceptions, of course, since this is tax law.
• Long-term gains on collectibles—such as stamps, antiques, and coins—are taxed at 28%, unless you're in the 10% or 15 % or 25% bracket, in which case the 10% or 15% rate or 25% rate applies
• Long-term gains from stock sales by children under age 19—under age 24 if they are students—may not qualify for the 0% rate because of the Kiddie Tax rules. (When these rules apply, the child’s gains may be taxed at the parents’ higher rates.)

Capital Gain Tax Rates 

why if $700K in LTCG is AGI only $200K. 

$200K less say a standard deduction of about $12K that leaves taxable income of about $188K. and assuming filing status is single. 

About $40K is taxed at zero leaving about $148K taxed at 15%.  so taxes would be about $22K.  but since key info is missing the taxes could be substantially different. 

MFJ about 80K taxed a zero leaving $108K taxed at 15%

Thank you, Mike. I guess I asked the question the wrong way. You are correct the AGI will not be $200K but $900K (200K would have been the AGI without LTCG). My question then is this: Is all of the LTCG of 700K taxed at the top rate, or is some (around 300K) of it taxed at a lower rate (15%) and then what is left at 20% (given that what is left means the total AGI is now above 500K, which is about the tax bracket threshold for married jont)?