Upon which things did Shakespeare depend when he wrote his plays?
Your question is very broad. In fact, it is so broad that it is it almost not possible to answer because I am not sure where your interest lies. When you ask about what Shakespeare depended upon, do you mean, "Upon what sort or type of audience did he depend to see, experience and appreciate his plays?" Do you mean, "Upon what sort of source material and/or stories, characters and themes did he depend?" Do you mean, "Upon whom did he depend to back and support his work financially, so that he could make a living as a theatre artist and playwright?" This list could go on, so you can see how tricky it is to hone in on a useful answer to your question.
I will say that he definitely depended upon his own modern day audience, the citizens of London in the late 16th, early 17th centuries, to enjoy his plays and return again and again to pay their entrance fee and fill the audience. He was a working man with a family back in Stratford-upon-Avon to support. So, if I had to choose a general answer to your question, I would say that thing he depended most upon was that he would be supported financially, both by his patrons (which, over time, included the Lord Chamberlain in Queen Elizabeth's court and King James himself) and by the ticket-buying audiences who attended his plays.
Enotes actually has quite a lot of information on Shakespeare and his plays. Please follow the links below for more information that might answer the more detailed interests you have.