What happens when transferring bitcoins to no address? What happens on the blockchain if I try to transfer bitcoins without providing  a recipient address?
Most wallet software won't let you send to a null address. If you have a transaction without an output script, that's invalid and won't be accepted by the network. If you have an output script that's simply an OP_RETURN or otherwise unspendable, those coins are lost forever.

Generally, you should be using a wallet to transfer bitcoins and if you don't provide an address using a wallet, you'll most likely not be able to send it.