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We introduce a new family of Generalised Parton Distribution models able to fulfil by construction all the theoretical properties imposed by QCD. These models are built on standard Parton Distribution Functions and extended to off-forward kinematics through a well-defined procedure. We apply this strategy on the pion, first handling a simple but insightful algebraic model, and then exploiting state-of-the-art computations obtained in continuum QCD. We compare these models with a more standard one relying on an xFitter extraction of the pion Parton Distribution Functions. The results for both quark and gluon Generalised Parton Distributions are presented and exploited for calculation of Electromagnetic, Gravitational and Compton Form Factors. Results on the latter highlight the relevance of next-to-leading order corrections, even in the so-called valence region., Comment: 20 pages, 12 figures