Network routers must be specially configured when they are first installed. Like computers and other devices on the home network, routers must be set up with IP addresses. Routers also offer optional, but strongly recommended, security features that can be set up if desired.
Normally you can connect your printer to the router using a USB cable or a USB-to-Ethernet cable. Alternatively, wireless print server hardware also exists. A print server connects to your printer's USB jack and in turn makes a WiFi connection to a wireless router. A few routers contain built-in print server capability, providing a built-in parallel port for cabling a printer directly.
In WiFi networks, routers can be joined with other devices (called range extenders or signal boosters) that increase the overall reach (range) of the wireless signal. Some people do this to share their home network with a neighbor. Wireless routers can sometimes be connected to each other for a similar purpose, but care must be taken to avoid conflicts or interference between the two devices.
Using a splitter will not create a new hub or router port. It merely helps cut down on the amount of cabling reaching the hub or router.
There are many companies that sell network splitters. You just have to know what you are trying to accomplish with your network and how many devices (computers) you are trying to install on the network.