As a method of producing RFID tags, printed graphene provides a low-cost and eco-friendly alternative to the etching of aluminum or copper. The high resistivity of graphene, however, sets a challenge for the antenna design. In practice, it has led to using very large antennas in the UHF RFID far field tags demonstrated before. Using inductive near field as the coupling method between the reader and the tag is an alternative to the radiating far field also at UHF. The read range of such a near field tag is very short, but, on the other hand, the tag is extremely simple and small. In this paper, near field UHF RFID transponders with screen-printed graphene antennas are presented and the effect of the dimensions of the tag and the attachment method of the microchip studied. The attachment of the microchip is an important step of the fabrication process of a tag that has its impact on the final cost of a tag. Of the tags demonstrated, even the smallest one with the outer dimensions of 21 mm * 18 mm and the chip attached with isotropic conductive adhesive (ICA) was readable from a distance of 10 mm with an RF power marginal of 19 dB, which demonstrates that an operational and small graphene-based UHF RFID tag can be fabricated with low-cost industrial processes.