An Access point can HANDLE more than one connection, but cannot split it.
A HUB, also does not split a single connection.
A ROUTER (cable router / broadband router - technically, a NAT Router) does the splitting... it also tend to be combined with a 4 port hub (typical wired router), or a hub and Wireless (Wireless router).
Once you have a router at the start of the chain, you can add wireless, extra hubs etc. - only a single router is needed.
You can also use a spare PC with a couple of ethernet interfaces as a Linux Router - the "Linux Router Project" has some basic setups.
http://www.linuxrouter.org/ - rest in peace, development stopped
http://leaf.sourceforge.net/ - a bit more promising
There are quite a few router/firewall projects that could use an old PC, but the little router boxes are normally fanless and silent... who wants an old PC humming in the background?