Comment on Start investing in mutual funds @ Zerodha

Hi Team,
I want to transfer my demat account from ICICI Direct to Zerodha — I have already invested with in ICICI Direct in Equity and Mutual funds (DSP, Mirae, Reliance) (I’m not the day trader).
Please explain the process, time taken for change and any charges.
Is it possible to maintain two demat accounts till Zerodha having full access on above mentioned mutual funds.

Thanks in advance.

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