Welcome to ƀ.com!
The name of this domain is ƀ.com; it is an Internationalized Domain Name (IDN). According to the Unicode standard, the name for the ƀ character is "Latin small letter b with stroke". One way to reach this domain is to type the punycode representation xn--lha.com in your browser bar. The Unicode code point for this character is U+0180.
Because the capital form, Ƀ, was added to the Unicode standard fairly recently (version 5 in 2006), not all application software handles it properly. In particular, many unicode-to-punycode convertors try to convert Ƀ.com to xn--5ma.com, rather than to the correct xn--lha.com. In other words, they treat Ƀ as a unique character rather than as the upper-case form of ƀ.
So if you put Ƀ.com into your browser's URL bar, only Opera (as of March 2013) will correctly take you to this site, ƀ.com. Other browsers (Internet Explorer, Google Chrome, Mozilla Firefox) will try to take you to xn--5ma.com, which does not exist and cannot exist.
Likewise, if you try to register the domain name Ƀ.com, your registrar's software will likely attempt to register xn--5ma.com, which is invalid. Of the registration/whois tools we have tried, only domaintools.com does the correct conversion of Ƀ.com to xn--lha.com.
Of course, if you try to register ƀ.com, you will discover that it is already registered.
Questions? Contact firstname.lastname@example.org