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Let $X$ be a smooth complex projective variety such that the Albanese map of$X$ is generically finite onto its image. Here we study the so-called eventual$m$-paracanonical map of $X$ (when $m=1$ we also assume $\chi(K_X)>0$). We showthat for $m=1$ this map behaves in a similar way to the canonical map of asurface of general type, while it is birational for $m>1$. We also describe itexplicitly in several examples.

The eventual paracanonical map of a variety of maximal Albanese dimension