(CNN) It's been less than two days, but one storyline of the Senate impeachment trial of Donald Trump has already emerged: Democrats are leaning heavily on California's Rep. Adam Schiff to make the case against the President.

Schiff spoke for two hours straight on Wednesday afternoon -- as the opening arguments by the House impeachment managers got underway. And it was Schiff who handled the press availability before Wednesday's proceedings -- even when the questions weren't directed at him.

To wit: CNN's Manu Raju tried to ask House Judiciary Chairman (and fellow impeachment manager) Jerry Nadler of New York a question about his decision on Tuesday night to accuse the Trump White House (and Republicans) of a cover-up in the Ukraine investigation. Schiff, with Nadler standing silently by, told Manu : "I'm going to respond to the questions."

So, OK then!

The primacy of Schiff in the Senate trial comes after a House impeachment investigation in which the Californian -- and the Intelligence Committee he chairs -- were front and center, conducting the interviews with key witnesses in both public and private. That was a contrast to the way in which the investigation into Richard Nixon was run, with the House Judiciary Committee handling the bulk of the work in that situation.

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