  We develop in this work a general version of paracontrolled calculus that
allows to treat analytically within this paradigm some singular partial
differential equations with the same efficiency as regularity structures. This
work deals with the analytic side of the story and offers a toolkit for the
study of such equations, under the form of a number of continuity results for
some operators. We illustrate the efficiency of this elementary approach on the
examples of the 3-dimensional generalised parabolic Anderson model equation and
the generalised KPZ equation driven by a (1+1)-dimensional space/time white
noise.
