Is there any limit to the complexity of objects that an abiotic process can construct in abundance? This question is of importance to biosignature science, but a central challenge has been finding a physically meaningful measure of complexity that can be measured in the lab. Recently, the Assembly Index defined as the smallest number of recursive joining steps to assemble an object, has been shown to be experimentally measurable for molecules. The assembly index along with copy number of objects form the foundations of observables in Assembly Theory [Sharma et al, 2023], which aims to quantify how much selection was necessary to generate a given configuration of objects. Applied to life detection, assembly theory was empirically demonstrated to distinguish chemical products derived from biological and abiotic samples [Marshall, et al. 2021]. Though the empirical results seem to place an upper bound on abiotic complexity, it is not yet possible to generalize from these measurements to environments beyond Earth without an explanatory model. Here we present an approach for calculating an object’s assembly path length distribution, where an assembly path refers to a minimal sequence of assembly steps which build an object, and the expected path length is the mean of the distribution. We show, in the absence of any constraints, the expected path length scales exponentially with the assembly index. This allows us to describe the existence of two scaling regimes, one where expected path length scales exponentially with assembly index, and with sufficient constraints to lead to a linear scaling. An abrupt transition between the two regimes would be indicative of a selection-mediated phase transition.