Sometimes, when a spell or ability resolves, part of what it does is impossible to do. In these cases, the following rule applies:
609.3. If an effect attempts to do something impossible, it does only as much as possible.
I understand that. But what if some effects on the card depend on what you did, when you didn't do what you couldn't do. Most of these effects will not do anything, because you cannot do anything with a card you couldn't reveal from an empty library. But some have effects that you could still perform. An example: Merfolk Branchwalker reads:
When Merfolk Branchwalker enters the battlefield, it explores. (Reveal the top card of your library. Put that card into your hand if it's a land. Otherwise, put a +1/+1 counter on this creature, then put the card back or put it into your graveyard.)
So what if this effects resolves, when you have an empty library? Obviously no card is not a land card, but is the +1/+1 counter put on it? Or is this effect just skipped because it depends on an effect that could not be done? What about cards that care about any values (cmc, power,...) the card has? Are they just interpreted as 0?
Some other examples include Counterbalance and Candles of Leng. There might be examples outside of effects that affect the top of your library, but I didn't find any unclear ones.