A common mistake, usually made by junior researchers, is to try to publish as a sole author. It is a mistake because a senior co-author, e.g. your supervising professor, will bring you citations. This should be your real objective and not to see your name in print, albeit with zero citations. Our reading time becomes scarcer and scarcer, while at the same time, we are drowning in information and new publications. Many people will read a paper co-authored by a famous professor, but very few (if any) will read one by a relatively unknown young researcher, no matter how good her paper might be.
A senior co-author brings another benefit onboard: most probably, he is also a seasoned writer and, as I discuss below, writing is an ‘art’ which takes years to master. A common reason for rejecting a paper is poor English and writing style, notwithstanding how good the paper might be content-wise.
Some authors of joint papers are often quite keen to appear as ‘corresponding authors’, believing that readers will assume that she is also the main author. This is not true. MEL for example does not report corresponding authors and when it does it makes it clear that a ‘corresponding author’ is just the one who exchanges emails with the EiC. As regards author order, in MEL and many other journals, most of the time, co-authors appear in alphabetical order of family name. MEL assumes that all co-authors are equally and indistinguishably responsible for the paper. If this is not the case, and thus authors require a different author-order, the journal may need to explain ‘respective roles’ in a headnote.
Outside our triennial PhD competition, MEL is rather cautious in publishing papers co-authored by PhD students, unless the supervising faculty member explains clearly the respective roles in the Cover Letter. In this light, and before submitting, the graduate student should make sure that her co-author is a ‘real’ co-author and not one who has just lent his name; your editor will see this immediately, and in most cases, this will lead to a negative decision.