why is my starter staying ingaged after replacing it along with cables and starter relay

If the starter was still engaged when you shut off the engine, it was engaged the entire time, you probably didn't realize it. Remove the starter from the vehicle. Reconnect the wires in the proper way. Have someone turn the key to the "on" position. The starter should do nothing. If the starter begins to spin in the "on" position it means you have power to the starter when you should not. Begin checking connections backward up the line until you find the defective wire/relay/solenoid then replace.

Also, if the starter begins to spin when the key is in the "off" position, or not inserted at all, just connected to the battery, begin checking backward also. You could also have a problem inside the ignition switch if the starter spins with only the battery connected and no key in the vehicle.