Equity question

[J White]

If a person has been living in a parent financed home, he/she provided the down payment and made all home payments and is the primary occupant, has recently refinanced the home (6 months ago), adding his/her name to the title along with a parent . If he/she sells the home now, will the equity be taxed as capital gains?And, could he/she claim all the equity even though there is another person on the title and loan?Basically I need to know how equity is split when a home sells.Is it between the owners or does the law make them split 50/50?