Einheri is right.
BJJ is rooted entirely in Judo, not Traditional Jiu-jitsu.
Except for the modern guards and some technical embellishments, all the original Gracie stuff came direct from Judo, even if they weren't legal for shiai.
Except for the Kodokan being fussy about exporting it to Brazil, it would probably be called Brazilian Judo (and have the unfortunate abbreviation of "BJ") except for Count Koma being prevented from using the word "Judo" when he went over.