The current is maximum through those segments of a circuit that
offer the least resistance. But how do electrons know beforehand
that which path will resist their drift the least? This is
really the same as Adam's answer but phrased differently.
Suppose you have a single wire and you connect it to a battery.
Electrons start to flow, but as they do so the resistance to
their flow (i.e. the resistance of the wire) generates a
potential difference. The electron flow rate, i.e. the current,
builds up until the potential difference is equal to the battery
voltage, and at that point the current becomes constant. All
this happens at about the speed of light. Now take your example
of having let's say two wires (A and B) with different
resistances connected between the wires - lets say $R_A \gt
R_B$. The first few electrons to flow will be randomly
distributed between the two wires, A and B, but because wire A
has a greater resistance the potential difference along it will
build up faster. The electrons feel this pote