Accretion is the drawing of matter into an astronomical body by Gravity, e.g., a star drawing matter, such as a Binary Star drawing matter from its companion. Black Holes also accrete matter, and in both cases, lead to observable phenomena. Accretion by forming Planets is considered a key part of Planet Formation.
The Accretion Rate in mass per unit time is used in calculations regarding Accretion Disks and other phenomena.
Accretion can result in heat as the release of the Potential Energy due to the gravitational force between the accreting matter and the body to which it is falling, which is called the Accretion Luminosity. A Maximum Accretion Rate (Eddington Accretion Rate) can be calculated by assuming that Black Body radiation from the accretion-generated heat creates Radiation Pressure against the fall of the accreting matter, and assuming the phenomena is spherically symmetric and steady-state. Higher accretion (Super-Eddington Accretion) could be achieved if all these assumptions do not apply, and may explain some apparently very bright sources.
Runaway Accretion or Accretion Runaway refers to situations where some usual mechanism for regulating accretion doesn't occur or is nullified and accretion becomes relatively rapid until some other mechanism puts a stop to it (which in some cases could be the eventual absence of material to accrete). The terms are used for a number of phenomena including planet formation (e.g., Gas Giants), Star Formation, and some stages in the evolution of stars.
The concept of Pebble Accretion is associated with planet-formation theories, consisting of a Planetesimal accreting objects (pebbles) on the order of a centimeter to a meter in size within a Protoplanetary Disk.