What is the ruling on child custody in the absence of the father?

In the U.S. child custody is determined by the courts and in the event of death or imprisonment of the father the children are given to the mother. In Islamic rules, in the absence of the father the paternal grandfather receives custody of the children. In cases where the mother is able to care for her children is it wrong for her to do so?
Concise answer
Grand Ayatollah Khamenei’s response
According to Islamic principles, assuming a child’s father passes away, the right to having custody of the child is, also, awarded to the mother up until the child attains the age of puberty. On occasions where the father is absent [for any given reason], such an absence does not nullify his right of custody, albeit unproblematic for the mother to take care of the child.
Grand Ayatollah Fazel Lankarani’s response
From a fiqhi (jurisprudential) perspective, the mother is awarded custody of the child – once the father passes away – even though the child’s grandfather is regarded as his/her automatically-ordained guardian. The latter cannot take the child from his/her mother.
Grand Ayatollah Makarim’s response
Assuming the grandfather’s guardianship and custody of the child, in question, is not feasible, awarding the mother with custody will be unproblematic; however, if it is feasible, the mother ought to acquire the (paternal) grandfather’s consent (vis-à-vis the child’s custody).
Grand Ayatollah Bahjat’s response
The ruling vis-à-vis the father’s absence or imprisonment is on a par with his demise i.e. the mother is awarded custody albeit not regarded as her inheritance.

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