Short answer. Each new owner bears it on the part that corresponds to him. Article 618 makes easements indivisible: dividing the servient estate does not modify the burden, it just distributes it. The lots the way actually crosses carry it; the ones it does not touch are unaffected in practice.
What the law says
Easements are indivisible. If the servient estate is divided between two or more persons, the easement is not modified, and each of them must bear it on the part which corresponds to him.
Civil Code, Article 618 — Easements Are Indivisible. Read the full provision →
Indivisible means the burden cannot be diluted
The word is doing precise work. It does not mean every resulting lot is equally encumbered; it means the easement itself cannot be split into fractions, reduced or reshaped by an act the dominant owner had no part in. He keeps exactly the passage he had. Where the way runs across only one of the new parcels, that parcel's owner bears it in full and the others are simply not on the route. What nobody may do is argue that because his share of the original land is now smaller, he owes a smaller version of the servitude.
Dividing the dominant estate is treated differently, and generously
The second half of the article covers the mirror situation. Where it is the dominant estate that is divided, each of them may use the easement in its entirety — every new owner gets the whole right, not a share of it. But two limits are attached, and they are the whole protection of the burdened owner: the place of use cannot be changed, and the easement cannot be made more burdensome in any other way. So four households may now use a passage one did, provided the route is the same and the intensity does not turn a farm track into something else.
Where subdivision disputes actually go wrong
Not in the law but in the plan. A subdivision drawn without reference to an existing servitude produces lots whose boundaries cut across the way, driveways that end at somebody's new fence, and buyers who were never told. None of that alters the easement — it survives the paper — but it guarantees an argument, and often a buyer with a claim against the seller who sold him an encumbered lot described as clean. The encumbrance should appear on the plan and in each deed before the parcels are sold.
Check the annotation, then the ground
Pull certified copies of the mother title and each derivative title and read the annotations, since a registered easement carries forward and an unregistered one may still bind those who knew of it. Then have the way located on the approved subdivision plan by survey, because the practical question — which of the new owners is the servient owner now — is answered by where the route falls, not by who was named in the original grant. Keep the instrument creating the easement; its wording fixes the width and the permitted use.