Question:

My Iranian friend told me that muta can be done without the permission of parents. Is that jaiz?

Answer:

If the girl is baaligh and mature, but a virgin, and her wali-e-shari’i (shari’i guardian) i.e. father or grand father is alive, then according to the researcher Shia jurists, permission of the wali-e-shari’i is necessary.
However, a girl can get married without the permission of wali-e-shari’i:

1. If she is not a virgin but a divorcee or a widow
2. If she is a virgin, but her wali-e-shari’i is not alive

And Allah Knows the Best!