The biggest challenge they will have is with parental responsibility, which is the major long-term decision-making element of parenting - consent for passports, major medical interventions, name changes, etc.
If they want, they can draw up consent orders granting the aunt sole parental responsibility and file it with the court, but I can't say with confidence that a court would seal them because it might not consider it in the child's best interests.
The other option would be adoption.