We present a description of a Monte Carlo algorithm that solves the modified DGLAP-type evolution equation in QCD. The change with respect to normal DGLAP is in the form of the argument of the coupling constant. We consider primarily the CCFM-like form \alpha (kT), but also a simpler choice \alpha (Q(1-z)) is discussed. The evolution is performed in the rapidity space with strict rapidity ordering and no gaps in phase-space.
PACS numbers: 12.38.--t, 12.38.Bx, 12.38.Cy
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