Many parents facing the prospect of a divorce or break-up where children are involved place a great deal of importance on obtaining "sole physical custody" or "joint physical custody" of the child or children. Parents are often devastated to find out that their former significant other is seeking sole physical custody, as if that phrase automatically means that there is an intent to preclude one parent from the child's life. These phrases have unfortunately taken on pop culture definitions that more often than not vary from reality.
Physical custody refers to where the child lives. If a child lives primarily at one place, usually thought to be about two-thirds of the time or more at the same residence, that child is considered to be in the "sole physical custody" of the parent who shares that address. Usually, children who are living in the sole physical custody of one parent have some sort of "visitation" schedule with the "non-custodial" parent. The details of that visitation schedule, also sometimes called a "parenting plan", are dependent on both parents. For some "non-custodial" parents it is every other weekend, for others it could be two or three days each week.
Even a parenting plan that falls into that two-thirds vs. one-third mold still includes a significant amount of time that the children are with the "non-custodial" parent.
In addition, not having sole physical custody does not mean that a parent cannot be involved in major life decisions involving the child. Or put another way, non-custodial parents are still able to contribute to the major life decisions necessary for their child. The ability to be involved in such decisions is determined by which parent or parents have legal custody of the child. In other words, while the sole physical custodian of the child may decide what clothes your child will wear to school, legal custodians can (and in most cases should) still be involved in decisions such as who the child's doctor will be, whether or not your child will have surgery, and what school the child will attend.
Finally, absent a restraining order or other order of the court to the contrary, all parents have the right to attend their children's public events, such as sporting events, concerts, etc. Most courts do not consider these types of public events the exclusive time of either parent. Although how you interact with the other parent at these events may depend on your ongoing relationship and the appropriateness of said interaction, it is usually still beneficial for a child to know that both parents are there cheering them on, even if separately. While this is not necessarily "quality time" with your child it remains another way non-custodial parents can remain involved in their children's lives.