Mortgage Brokers are "signed-up" or appointed with lenders.  These appointments can range from a dozen to perhaps 100 or more.  There is no public list that discloses appointments as such appointments are made directly between the lender and the broker.  The lender has a set of compliance requirements to qualify for an appointment such as a broker license in the particular state of practice, years of experience, verifiable volume of transactions, verifiable assets and other requirements.

The question, however, seems to raise an element of distrust with the broker.  If so, it is wise to quickly address any concerns of integrity, competence, accuracy or timeliness up-front and directly with the broker.  On the other-hand, by disclosing your rational for determining the lender appointment list in your question through this forum, I may be able to provide you with a better reply.

With today's market the number of players have dwindled. Most brokers use the same wholesale broker. Make sure when your shopping for a mortgage to get everything in writing. Even with all of the forms you sign remember that they are just estimates. While many of the "bait and switch" brokers have gone on to other things it is important for you, the customer to get written guarantees about fees and rates. 

Now if there is a specific lender you do not want to use just let your broker know this up front. I am sure they will work it out so you are satisfied.

Remember that most mortgages today will get sold off within a few months of signing with them. In the long run you will be OK. Please let me know if you have any additional questions.