Does paternity leave actually exist or is it just a thing HR talks about?

Used up my official "paternity leave" (2 weeks, corporate job, major city). Half that time I was still answering emails because "things came up." Could my boss legally require that? Probably not. Did he ask real nice and make me feel like I should? Yeah.

Looking at new jobs partly for this reason. Somewhere that doesn't say they value fathers being present but actually means it.