Manufacturers of inks and pigments are not required to reveal the contents. A professional who mixes his or her own inks from dry pigments will be most likely to know the composition of the inks. However, the information is proprietary (trade secrets), so you may or may not get answers to questions.
Most tattoo inks technically aren't inks. They are composed of pigments that are suspended in a carrier solution. Contrary to popular belief, pigments usually are not vegetable dyes. Today's pigments primarily are metal salts. However, some pigments are plastics and there are probably some vegetable dyes too. The pigment provides the color of the tattoo. The purpose of the carrier is to disinfect the pigment suspension, keep it evenly mixed, and provide for ease of application.
Tattoos and Toxicity
This article is concerned primarily with the composition of the pigment and carrier molecules. However, there are important health risks associated with tattooing, both from the inherent toxicity of some of the substances involved and unhygienic practices. Some of the risks are described in this article. To learn more about these risks, care of a new tattoo, and get other information, check out some of the sites listed to the right of each page of this article. Also, check out the Material Safety Data Sheet (MSDS) for any pigment or carrier. The MSDS won't be able to identify all chemical reactions or risks associated with chemical interactions within the ink or the skin, but it will give some basic information about each component of the ink. Pigments and tattoo inks are not regulated by the US Food and Drug Administration.
Tattoo Pigment Chemistry
The oldest pigments came from using ground up minerals and carbon black. Today's pigments include the original mineral pigments, modern industrial organic pigments, a few vegetable-based pigments, and some plastic-based pigments. Allergic reactions, scarring, phototoxic reactions (i.e., reaction from exposure to light, especially sunlight), and other adverse effects are possible with many pigments. The plastic-based pigments are very intensely colored, but many people have reported reactions to them. There are also pigments that glow in the dark or in response to black (ultraviolet) light. These pigments are notoriously risky - some may be safe, but others are radioactive or otherwise toxic.