This work introduces the Generalized Low Density Parity Check (GLDPC)-Staircase codes for the erasure channel, that are constructed by extending LDPC-Staircase codes through Reed Solomon (RS) codes based on "quasi" Hankel matrices. This construction has several key benefits: in addition to the LDPC-Staircase repair symbols, it adds extra-repair symbols that can be produced on demand and in large quantities, which provides small rate capabilities. Additionally, with selecting the best internal parameters of GLDPC graph and under hy- brid Iterative/Reed-Solomon/Maximum Likelihood decoding, the GLDPC-Staircase codes feature a very small decoding overhead and a low error floor. These excellent erasure capabilities, close to that of ideal, MDS codes, are obtained both with large and very small objects, whereas, as a matter of comparison, LDPC codes are known to be asymptotically good. Therefore, these properties make GLDPC-Staircase codes an excellent AL-FEC solution for many situations that require erasure protection such as media streaming.