In the episode " One Day Like This " (Season 14, Episode 17), the "paper" refers to a legal document (a "deed") and instructions that Dr. Nick Marsh hands to Meredith Grey .
This gesture underscores the immediate and deep emotional connection between the two characters, as Nick trusts a woman he has just met with the most important aspects of his life. [S14E17] One Day Like This
See the first meeting between Meredith and Nick Marsh that led to this moment of trust: In the episode " One Day Like This