The different Human computer networks are assembled in what it called WideNet. It's first consist of planetary networks (called LocalNet) linked by communications lines. Then you get the StellarNet linking the different planetary networks (including those hosted by Space stations orbiting worlds). And finally there's the overall network linking the different StellarNets.

A network could be public (free access for everyone) or restricted (private networks owned by governments, corporations...).

The communication lines use mainly Radio, Laser or Maser relays for routing. These communications lines are manned by Access provider companies, depending of their infrastructure, you could access to all or only a part of the WideNet.
In the Stellar age the distance between two networks slows considerably the transmission of information. Even maser communications can't go faster than lightspeed and it's not common to get delays if you want an information stored at the other end of the stellar system. To ease delay calculation consider that light travel at a rate of 1 A.U. per 10 minutes. So if you're on Earth and want to logging on Saturn network, you'll need to wait 85 minutes! It's really stressing if you want only to browse through a travel catalog or worse if you want to launch a job on a distant supercalculator waiting 170 minutes between each command (85 min to send the command, and 85 min to get the result).
This delay is superseded by regular copy of the distant network on a local node. Of course, only public datas are copied, you don't want your top secret informations stored on a computer owned by another one, don't you? Between two full copies, some providers add incremental copies (copy of new and altered files). The time between two copies varies from one per hour to one per month, depending on the network importance and popularity.
Not all local networks are backed up, the amount of storage needed could be really huge, even for a high-tech civilization. So you need to use catchers programs to retrieve informations on distant networks. You group all your requests, and the catcher program is doing the job for you, informing you when it's done.

For extra stellar communication, distance involved are important even with lightspeed, if light needs 10 years to travel to a star, your email when arrived could be really outdated. So the trick is to use wormholes. Communications can't directely travel through wormholes, instead any emails, network backups or net requests are stored on "securized" memory devices that are transported by a drone (or even line freighters) making frequent trips through the wormhole. With this system, the communication delay between two distant systems is more tolerable. For simplicity, let rules that it takes 10 hours for an information to travel to a system linked by a wormhole.
Sending a restricted data through the WideNet could be very risky, you need to use a communication line owned by a third party, sometimes your datas are transported by a starship line company, and if your destination is far away it could transit through several access providers. Don't need to say that crypted datas are an obligation. Even if access providers have a duty of confidentiality (a provider caught of highjacking datas will certainly see all its users defecting), paranoiac users prefer to use their own courrier ship when dealing with sensitive data (data alteration is a common fear). It's why there's often an inhabited space station near a wormhole.

This article could apply to any other high-tech Babel race.