An effect that replaces a card draw is applied even if no cards could be drawn because there are no cards in the affected player’s library.
May 3, 2019 · War of the Spark
If an object enters the battlefield with counters on it, the effect causing the object to be given counters may specify which player puts those counters on it. If the effect doesn’t specify a player, the object’s controller puts those counters on it.
January 25, 2019 · Ravnica Allegiance
If an object enters the battlefield with counters on it, the effect causing the object to be given counters may specify which player puts those counters on it. If the effect doesn't specify a player, the object's controller puts those counters on it.
April 28, 2017 · Amonkhet
If an object enters the battlefield with counters on it, the effect causing the object to be given counters may specify which player puts those counters on it. If the effect doesn’t specify a player, the object’s controller puts those counters on it.