What kind of taxes are applicable in CA if the property of my father is left to a trustreeship at his death?

First its not a good idea to piggyback your question on someone else's. This can lead to confusion. You should start a new thread. So I've moved your question to its own thread.

Whether the beneficiary of the estate is a trust or an individual shouldn't matter. If the value of the estate is over the $2M threshold, the estate has to pay taxes BEFORE the property is turned over to the trust.

The trust administrator will take care of estate duty. There is no estate duty if the estate is less than 2 million.
There is no federal tax and CA tax on inheritances.
Read: Your U.S. Tax Return: Tax on Inheritances