I am currently working on OPT and it expires this August. However I have applied at few universities for phd programs for this spring. Since my OPT expires in August 30. I know I have the 60 day grace period which will end in October 30th. Should I get accepted to the PHD program in Spring and get the I20 would i have to go back home and come back for spring. Or can stay here legally till the spring semster starts in January. 

Thanks
Samrat

as far as i know you transfer your F1 , in opt you are still under F1 under your school so  when you go to another school you transfer your F1.

 maile ni tai suneko thiye subbu didi

You can stay here and don't need to go outside of US....if you want to go outside and you don't have valid visa or visa ending soon you may get in trouble...

So, 60 days from OPT expiration you have to do the sevis transfer to different college and your program should start with 90 days of the transfer.

College transfer time:till Oct 30th.
Semester start time:Jan 30th.

GL.