Brooke Hogan is breaking her silence on Hulk Hogan's death ... and she's clearing up a few things involving their relationship.
Hulk's daughter just posted a long statement on social media, the first time she's spoken out about his passing ... and she says, "We had a connection deeper than words, one that spanned lifetimes."

Brooke says Hulk lives on through her and her children -- including a daughter who bears his middle name, and sometimes, his scent -- and she says she's grateful she knew the real HH a not just the one the "world viewed through a carefully curated lens.