In this paper, we propose a model for the analysis of distributed passive backscattering systems for Radio Frequency Identification with physically separated illuminator and reader. The model takes into account the physical channel characteristics including shadow fading components and thresholds for powering and detection. The dynamic framed ALOHA medium access mechanism defined by the EPC Global Generation 2 standard is considered to evaluate the performance. To address the complexity of the system model, our framework is based on a semi-analytical approach that combines moment matching approximation method at channel level and Monte-Carlo approach for the medium access control dynamics. Results show the impact of deployment conditions and the relative positions among illuminator, tags, and reader on the identification performance. Interestingly, the detection of the back-scattered signal at a remote reader can improve the performance with a higher probability of capture. However, as the distance increases, the impact of shadow fading counterpoises the capture effect. The resulting trade-off is accurately described by our model.