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"largely depending" is correct and usable in written English.
You can use it when you are talking about something that is mostly or to a great extent based on another factor or factor(s). For example, "The success of the project is largely depending on the dedication of the team."
Exact(60)
Prior local or regional studies of immigration, or of changes to immigration law, have found both positive and negative fiscal impacts, again largely depending on what and how economists chose to measure.
The answering and participation behavior can vary largely depending on culture [62].
However, the estimation error variance is largely depending on the channel noise.
Many rules of movement have been designed largely depending on conspecific effects.
Capacities obtained by the breakdown method vary largely depending on the traffic situation at a particular site.
Either way, the interviewees' perceptions about value co-creation varied largely depending on their degree of activity in the ecosystem.
Vehicle's powertrain performance and comfort are largely depending on the clutch control strategy for an Automated Manual Transmission (AMT).
These diatom frustule dimensions differed largely depending on diatom species with pore diameters d ranging from 0.3 to 3.0 μm.
The choice of an appropriate expression system remains empirical, largely depending on the biochemical and biological properties of the target proteins (Bernaudat et al., 2011).
However, the share of consumption is varies considerably, and largely depending upon the availability, the cost in terms of required time for collection.
The effects of drying and rewetting process on soil aggregate stability are inconsistent, largely depending on soil type, percent of stabilizer, test methods and curing conditions, as forementioned.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com