Arduino+Transmitter+Receiver

hi all,
I am currently working on an Arduino project and am currently successful in receiving accelerometer data from serial port to my computer.
I want to make it like this:
Arduino-->>computer(receiver)--->>another computer( connected by ethernet cable or internet)
I mean that I want to continuously stream data I am receiving from Arduino board from one computer to another.
Can you please guide me in the method to do is. I know that a software will be need to connect the two computers and continuously transmit the data. A detailed answer will be appreciated.
Thanks

What software are you currently using on your PC to receive data from the Arduino?

I'm wondering if you can extend that to send data to another PC

...R

I mean that I want to continuously stream data

What kind of data? How much data? Where does the data come from?

Vague questions deserve vague answers.