Even when Akshara was unconscious and weak, it would have made much more sense for Abhinav to inform her family of the situation(he could have used her phone to find the contact info) - any one in that situation might have done this as the first step. Family should be notified in emergencies - that's the first thing even hospitals do.
But since Akshara didn't want to reach out to her family and as its her truth to tell, Abhinav obliged regardless of what happened to Akshara - which given how they have portrayed Abhinav so far - just doesn't seem to add up. I want to feel sad for her for that stormy night story, but I just end up laughing at the script and story.
I am not aware of the legal process, if any, but wouldn't they try to find her family to handover the baby? She didn't have any documents but she was using her/Abhinav's phone to inform Abhimanyu and she contacted BP as well. Abhimanyu may/may not have responded but BP would take the call and come for the baby.
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