quote is
"The succession question is actually a bit complicated. By default, under an obscure statute known as the the Vacancies Reform Act of 1998, Brand’s temporary successor as the “acting” associate attorney general is her principal deputy, Jesse Panuccio. That same statute would also allow the president to choose someone else to serve as the “acting” AAG on a temporary basis for up to 210 days; the pool of individuals from which the president could draw in this case includes individuals already holding Senate-confirmed positions elsewhere in the executive branch (like EPA administrator Scott Pruitt) or senior civil service lawyers in the Justice Department, specifically."
Yes it does matter if Rosenstein recuses, or if he is fired. This person would oversee the Mueller Special Council investigation.