Transaction and Node Proximity Questions
You add the transaction T to your (the sender's) unconfirmed transactions pool. From there on, it is treated like any other transaction. Then, your client will send a "inv" message to it's peers saying it has a transaction with hash H. (H being the hash of T) If the peers don't have it, they will send a "gettx" message requesting it, and your client will send it to them. They then add it to their list of unconfirmed transactions and they will do the same thing with their peers.