Behave, conduct, comport, demean, deport, acquit, quit are comparable when they mean to act or to cause or allow (oneself) to act in a specified way or in a way that evokes comment.
Behave denotes the performing of various actions or the saying of various things in the manner indicated by modifiers.
Used without modifiers, it indicates action and conduct adjudged proper and seemly; in this use it is common in relation to children and adolescents.
Conduct often applies to actions showing direction or control of one’s actions or bearing with command, will, knowledge, and resolution.
Comport, in this sense always reflexive, is somewhat more formal than behave and conduct but usually lacks any other special suggestion though it sometimes may convey the notion of conformance to the expected (as of one’s class) or suitable (as to one’s position).
In this sense demean and deport are close synonyms for comport; the former is becoming rare. The latter may suggest deportment according to a code.
Acquit and quit, the latter archaic, are always used reflexively in this sense; they are likely to apply to action deserving praise or meeting expectations.