That would vary from state to state. Check with a local attorney.

One that doesn't fit

The definition of an unfit parent is governed by state laws, which vary by state. A parent may be deemed unfit if they have been abusive, neglected, or failed to provide proper care for the child. A parent with a mental disturbance or addiction to drugs or alcohol may also be found to be an unfit parent. Failure to visit, provide support, or incarceration are other examples of grounds for being found unfit. For example, one state declares the power of the juvenile court to terminate the rights of a natural parent (a) who was "unfit or incompetent by reason of conduct or condition seriously detrimental to the child," (b) who "abandoned the child," or (c) who "substantially and continuously or repeatedly refused or failed to give the child proper parental care and protection." Some state laws provide for a fitness hearing to be held after an adjudication of neglect, dependency or abuse. In such cases, the law may specify a time period after such an adjudication in which the parent may make efforts to resolve the problem, such as seeking drug or alcohol treatment. A parent's failure to make reasonable efforts and progress within the specifed time frame is a ground of unfitness. Local laws should be consulted for specific requirements in your area. The court will often award sole custody to the other parent when one parent is deemed unfit, or if both parents are deemed unfit, the child may be placed in foster care. Evidence of parental unfitness toward one child may be grounds for terminating the parental rights to other children even though the parent never abused or neglected those children. The best interest of the child is the determining factor.

An unfit mother is a mother who cannot provide the basic necessities that a child needs. What context are you asking? If you are simply asking about custody between parents, you should note that even if you are a fit parent, you could still lose custody if custody with the other parent is in the best interest of the child.

Definitions will vary by jurisdiction, but here is a "sanitized" universal definition which ignores moral grounds ... http://definitions.uslegal.com/u/unfit-parent/

hi, i am the father of my 3 week old daughter. how bad is it if the mother yells in front of the baby? can the custody be taken away from her if the father is calmly talking but the mother is always yelling while holding the baby?