  The formation of giant planets requires accumulation of ~10 Earth mass in
solids; but how do protoplanets acquire their mass? There are many, often
competing processes that regulate the accretion rate of protoplanets. To assess
their effects we present a new, publicly-available toy model. The rationale
behind the toy model is that it encompasses as many physically-relevant
processes as possible, but at the same time does not compromise its simplicity,
speed, and physical insight. The toy model follows a modular structure, where
key features -- e.g. planetesimal fragmentation, radial orbital decay, nebula
turbulence -- can be switched on or off. Our model assumes three discrete
components (fragments, planetesimals, and embryos) and is zero dimensional in
space. We have tested the outcomes of the toy model against literature results
and generally find satisfactory agreement. We include, for the first time,
model features that capture the three-way interactions among small particles,
gas, and protoplanets. Collisions among planetesimals will result in
fragmentation, transferring a substantial amount of the solid mass to small
particles, which couple strongly to the gas. Our results indicate that the
efficiency of the accretion process then becomes very sensitive to the gas
properties -- especially to the turbulent state and the magnitude of the disk
headwind (the decrease of the orbital velocity of the gas with respect to
Keplerian) -- as well as to the characteristic fragment size.
