Is it true that the mother is presumed to get custody of the child?

No. People may be thinking from the Britney Spears case that you have to drop your kids from your arms, drive without a license, be drunk in public, and be addicted to drugs before you can lose your kids. Not so. The question is who can provide the care that is in the best interests of the child. That could be both parents, or the mother, or the father, or, if neither one is a fit parent, someone else.