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A rashidah girl is one who can tell what is to her benefit and what isn't and her decision to get married isn't influenced by lust or feelings. This matter varies with different people, some may reach such an ability sooner than others, thus it is impossible to specify a certain age for it. 
Keeping this definition in mind, our respected maraje’ have different viewpoints on the necessity of the father of a virgin girl’s consent when getting married:
If a baligh virgin girl who is rashidah, meaning that she can tell what is to her benefit and what isn't, wants to get married, she must get her father’s permission (or her grandfather’s permission from her father’s side in the case of her father being deceased). But if she isn't a virgin and has lost her virginity through having another husband, her father’s permission is no longer required. 
Ayatullah Mahdi Hadavi Tehrani’s response:
Getting permission for a virgin girl who is rashidah (who well understands what is to her benefit and what isn't) must get her father’s (or grandfather’s) permission as a necessary precaution, although the stronger verdict on this issue (aqwa) is that it isn't necessary.
If the father doesn’t give permission while the marriage is to the girl’s benefit, his permission is no longer required. 
For further information, see:
2- Why the girl needs to get permission from her father for temporary and permanent marriage, Question 2074 (website: ).
3- Temporary marriage with virgin girl, Question 610 (website: ).