I'm going to try this on my Galaxy Tab 3 7". It will charge from my Galaxy S4 phone charger, which will also bring it up from a totally dead battery. But the tab will barely trickle charge from anything else, even a 2.1 amp Belkin iPad charger, and it won't come alive from a dead battery with anything but the S4 charger.
The phone will pull 460ma from a normal USB port and 1,900ma from the charger that came with it and the same from the Belkin charger. I assume the S4's charger has the 1.25V on the data lines. The Belkin charger must not or has iDevice compatible voltage on the data lines or they are simply shorted together. However it is, the Belkin does not output what the GT3 7" expects.
Now I have to cut the internal connector off the crappy aftermarket battery I bought for the GT3 to replace the original because one end of it broke off and apparently the contact that sends power to the circuit which monitors the power button is not making contact. The charge icon lights up and the original battery has been taking quite a while longer to charge off the S4 charger than the cheap replacement battery. Hopefully that's an indication it's actually 4,000mah and the cheap battery is considerably less. If I left it unplugged and off overnight the battery would be almost dead by morning. (Of course the GT3 7" is known for lousy power management, hopefully to be fixed *if* the GT3 7" ever gets Lollipop in the USA! Also waiting on Lolli for the S4. The rest of the planet has it on these, why don't we?!)
Had I known about Samsung's silly non-standard charging setup before I bought a supposedly genuine Samsung (black) charger off eBay (it went missing somewhere) and another white one - which I very carefully compared the printing in the images on eBay to my known genuine charger before ordering it... Only to find when I got it that it would barely charge my S4 and the tablet not at all, then it died. Closer examination showed the color of the text on the ersatz white charger was a slightly different color and the text size in the SAMSUNG logo was a slightly different size and the fake-o weighed a gram or so less. Would be nice if Samsung and eBay would crack down on all the sellers of counterfeit chargers!