I haven't been able to find an answer to this question in any small-
business books.

What happens to the legal entity of a (New York State) business
partnership when the partnership breaks up and one person buys the
other person out?  Does it 'automatically' become a sole
proprietorship?  What does the remaining partner need to do, legally
and for tax purposes, to continue working under the same business
name?  Please include references in your answer. Thanks.

I do not know if New York has the, or a variant of the, Uniform
Partnership Act on its books, but if it does, that uniform act defines
a partnership as a business venture for profit of "two or more
persons."  By definition, then, it cannot be a "partnership" with only
one person and the uniform act states that in such a case the
partnership is "dissolved" and must be "wound down."  So no, it does
not automatically become a sole proprietorship.  Once the partnership
is dissolved and wound down, however, you may continue to use the name
as a sole proprietor as long as you do not continue to hold that sole
proprietorship out as a partnership.

A note of caution--a dissociated partner may still ,under certain
circumstances, bind the partnership even after he or she is bought
out, so you should check with a New York lawyer about filing a
statement of dissociation and a statement of partnership dissolution.

Thanks for the comment.

I spoke with an accountant, who said that I don't need to re-file for
a DBA or other new york state paperwork, I can keep doing business (as
you said), and I will of course need to file a schedual C.

Just wanted to note that in case other people search and find my question...