Homozygous Tobianos:
A true homozygous Paint horse is always a tobiano. The homozygous horse has two identical tobiano genes and must be sired by a tobiano, and have a tobiano for a mother.
The true homozygous tobiano must have secondary body spotting called "ink spots" and "paw prints" and must never have produced any solid colored foals from solid colored mates.
Homozygous Tobianos will always pass a tobiano gene to an offspring (genes TT). The majority of homozygous tobiano stallions standing today, sire 100% tobiano paint colored foals from the mares they breed.
A few horses that are listed as homozygous, have sired the occasional solid breeding stock foal, but this is rare.
A horse shows all of the characteristic traits of homozygous horses with blue zones around the paw prints on his hip and withers and ink spots.
Ink Spots, Paw Print Markings:
These unique and distinctive markings are usually located in the 'white' hair areas on a tobiano and are small dabs of spots or color (1-3 inches) surrounded with prominent "blue zones" (white hairs on black pigmented skin that give the hair a blue appearance) surrounding the 'spot'.
Usually there will be groups of prints that look like dog or cat tracks. The black homozygous tobiano has nice examples of these markings.
These patterns tend to show up on homozygous individuals, who have two tobiano genes, but also occur on heterozygous tobiano horses who only have one tobiano gene.
Heterozygous Tobianos:
A tobiano foal who has one tobiano parent and one quarter horse parent can only have one tobiano gene, regardless of its markings and therefore, cannot possibly be homozygous, nor can it consistently sire colored foals. When genes at the same location are not the same, and the parent can pass either gene (Tt), the horse is considered to be heterozygous.
APHA link for more info on this topic and information on Lethal white syndrome.