Your license moves. Your database usually moves, subject to what you signed. Your active listings generally do not, because the listing agreement is between the seller and the brokerage rather than between the seller and you.
That last point is the one that catches people. If you have four active listings and you resign on a Monday, those listings stay with your old brokerage unless each seller asks to be released and the broker agrees. Some brokers release without friction. Some do not.
Pending contracts are usually finished at the original brokerage, and your split on them follows the agreement that was in force when they went under contract.