Depending adverbs are provided in this article. The words listed here are commonly found along with the verb depending in sentences. This reference page helps answer the question what are some adverbs that describe or modify the verb DEPENDING.
actually, apparently, chiefly, considerably, daily, differently
directly, dramatically, enormously, entirely, exclusively, greatly
heavily, immediately, largely, mainly, markedly, merely
mostly, partly, primarily, principally, probably, significantly
simply, slightly, solely, substantially, tremendously, usually
wholly, widely, wildly
Hope this word list had the depending adverb you were looking for. In addition to adverbs used with depending, other example verb adverb pairings can be found on this site.
You can help by adding more adverbs in the comments. Thanks.