What are the meanings of " has been home" and " public rows in this paragraph ?
More recently the northern English city of Manchester has been home to the Gallagher brothers - founders of the rock group Oasis whose What's the story Morning Glory? was the biggest-selling UK album of the 90s, and whose very public rows and outrageous behaviour often attracted more attention than their music.

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Answer

to be home to = to be the home of.  It's where the Gallagher brothers came from.

"public rows" is literal.  "row" in this case means argument. When you speak it, it sounds like "how".  But when you write it, it is spelt the same as row = line.