Do I transfer all of my property into my Trust?

Answer

Not necessarily.  Property and accounts which you own jointly with rights of survivorship are not transferred into your trust.  Likewise, any account or policy that lets you name a beneficiary to inherit upon your death do not get transferred into your trust.  If you want to ensure that an asset or account will be distributed to the beneficiaries you name in your documents, you should transfer that property or account into your trust.