  The aim of this paper is to show two applications of metric currents to
complex analysis. After recalling the basic definitions, we give a detailed
proof of the comparison theorem between metric currents and classical ones on a
manifold. In Section 3 we introduce the concept of bidimension for a metric
current on a finite dimensional space, showing that the usual properties of
$(p,q)-$currents still hold, except for the existence of a Dolbeault
decomposition. Section 4 is devoted to the analysis of a particular class of
complex spaces, whose structure allows us to give a structure theorem for
currents, solve the Cauchy-Riemann equation and characterize holomorphic
currents. In Section 5, we introduce the concept of bidimension of (global)
metric currents on a Banach space and relate it to the behaviour of the finite
dimensional projections of the currents. In section 6 we define a new class of
currents, the \emph{quasi-local} metric currents, which are usual metric
currents when restricted to bounded sets, and we give a definition of
$(p,q)-$current in this new class. The last Section shows how to employ these
newly defined quasi-local currents in order to obtain a solution to the
equation $\debar U=T$, when $T$ is of bidimension $(0,q)$ and its support is
bounded; finally, we extend the result to a current $T$ with generic
bidimension, $\debar-$closed, with bounded support.
