If two siblings each own half the house and one dies does the other inherit automatically the other half

First, please do not piggyback your question on another thread. I've moved your question to its own thread.

That depends on how the title reads. There are basically two types of ownership, Tenants in Common and Joint Tenants with Right of Survivorship. In the first, each owner is separate and their share of the property goes to their estate. In the second, ownership passes to the survivor.

This was actually explained in the thread you originally posted to, didn't you read it?