New kinetic effects on the model of two-dimensional screw lattice (2DSL) crystal are interpreted, which are caused either by different generation frequencies of new "layers" at the opposite edges of a crystal face (position-dependent effect) or by different rates of "layer" propagation in opposite directions (direction-dependent effect). Interactions between nearest and next-nearest building units are taken into account. The treatment is based on the different binding energies to the opposite apices and/or to the opposite oriented kinks on the crystal "surface". These effects can be visualised macroscopically by the morphology of unstable crystals. Their diffusion-limited growth (initiated at the apices) leads to asymmetric skeletal or dendrite pattern. A recently reported observation of screw-like weddellite crystals demonstrates experimentally the existence of such effects.