We present the e-TidalGCs project, aimed at modeling and predicting the extra-tidal features surrounding all Galactic globular clusters for which 6D phase-space information, masses, and sizes are available (currently numbering 159 globular clusters). We focus the analysis and presentation of the results on the distribution of extra-tidal material on the sky, as well as on the different structures found at different heliocentric distances. We emphasize the wide variety of morphologies found: beyond the canonical tidal tails, our models reveal that the extra-tidal features generated by globular clusters take a wide variety of shapes, from thin and elongated shapes to thick and complex halo-like structures. We also compare some of the most well-studied stellar streams found around Galactic globular clusters to our model predictions, namely, those associated with the clusters NGC 3201, NGC 4590, NGC 5466, and Pal 5. Additionally, we investigate how the distribution and extension in the sky of the simulated streams vary with the Galactic potential by making use of three different models, either containing a central spheroid, not containing one, or containing a stellar bar. Overall, our models predict that the mass lost by the current globular cluster population in the field from the last 5Gyrs is between 0.3-2.1x10^7^M_{sun}_. This amount is comparable to a value between 7-55% of the current mass. Most of this lost mass is found in the inner Galaxy, with the half-mass radius of this population being between 4-6kpc. The outputs of the simulations will be publicly available, coinciding with the unique opportunity presented by the delivery of the ESA Gaia mission and complementary spectroscopic surveys. Their exquisite data will offer the possibility to carry out novel comparisons with the models discussed in this work.