We present atomic force microscopy results and corresponding computer simulations on crystallization of quasi-2D monolayers of polyetheleneoxid adsorbed onto bare silicon wafers. Fingerlike branched patterns with a characteristic width $w$ resulted from crystallization at temperatures ${T}_{c}$ below the melting point ${T}_{m}$. $w$ decreased exponentially as $({T}_{m}{\ensuremath{-}T}_{c})$ increased. The patterns are explained by a simple model considering the interplay of transport on the surface and the probability of attachment to the crystal.