Before attempting to register a domain name at Network Solutions, read this article.
Apparently, Network Solutions takes the domain name that you enter and puts it on hold. This means that once you have seen that the domain you want is available at Network Solutions, if you want the domain you have to pay their relatively high fees ($34.99 for one year for a dot com) as compared to $9.95 for one year for a dot com here.
You can check this phenomena out for yourself by making up a name (that you are NOT interested in), trying it at another registrar. If it is available try it at NetworkSolutions.com, then go back to the original registrar and see if it is still available.
Some posts on this subject say that the hold is only temporary, so to be charitable to NetworkSolutions.com you could argue that they are doing you a small favor by restricting its registration from other registrars. However, if you happened to be in a race to register a domain name there would be nothing to stop someone else registering it at NetworkSolutions.com