What is episodic accretion in star formation? When I think about "episodic accretion", I imagine material from an envelope accreting only sometimes. Is that the right meaning of episodic accretion? or does it mean that the accretion rate is irregular? 
 A: "Episodic accretion" is the term that has been given to a hypothesis to explain the luminosity distribution of "class I" embedded protostars.
The idea is that these stars accrete via a disk from a more spherically distributed envelope. The envelope adds mass to the disk, which then become unstable on an irregular basis. The instability dumps extra material onto the protostar and the accretion rate and luminosity increase by an order of magnitude or more.
The mass of the star is therefore built up largely through bursts of accretion with a small duty cycle.
Some papers that address this subject can be found here: Baraffe et al. 2009; Vorobyov & Basu 2015.
Whilst the episodic accretion of matter onto protostars seems widely accepted, the physical and observational effects of that accretion are debated. My interest in this debate is whether the accreted material is "hot" or "cold" - that is whether it's gravitational potential energy is absorbed by the protostar or promptly radiated away. Hot accretion could give rise to FU  Orionis type outbursts, while cold accretion may cause a dispersion in the Hertzsprung-Russell diagram that is later interpreted as an age spread in coeval populations. 
