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Affairs can be a factor depending upon the circumstances of the case. Most of the time if the relationship was discrete and doesn't overtly or negatively impact the children, then it will be a non-issue.
It can become a negative factor, however, if the relationship somehow poses a harm or threat to the child or children, such as having harmful sexual overtones or something that puts the child or children in an embarrassing situation.
If there is a live-in partner involved with one of the parents, then the judge may take into consideration any effect or influence this person would have on the child/children and also the affect that this relationship would have with the non-custodial parent. As with most any other determining factor when considering child custody issues, the best interest of the child is the most important part of the court's decision making process.