I. Suppose you have a riparian land owner (A). By a deed of exchange, they trade to someone (B) an exclusive right2 to fish in the portion of the river opposite the lot, in exchange for some piece of land which is immaterial to the setup described. As subsequent sales by both (A) and (B) of their respective estate/rights occur, and ultimately the death of (B), questions arise:
- How do you qualify that fishing right? Is it an easement, profits-à-prendre; is that a full fledged fee simple or a mere interest arising out of a contract?
- Is it alienable/assignable?
- Can there be apportionment of the right?
- Does the right outlast the life of the original
Looking for a Restatement (Third) compliant answer if it's based on U.S. common law. One can assume the deed is ambiguous and therefore all the presumptions come into play except for the fact it mentions the grantee has an exclusive right to fish, that his intent is sport fishing, and that there is no dominant land whatsoever involved.
Expanding on the first question, whether those fishing rights include any interest whatsoever in the river bed or whether it is seen as a charge/burden on the land owner's (A) radical title is of particular interest (registration considerations may be discussed if pertinent).3
II. Since Restatement (First's), I read profits-a-prendre are subsumed into easements in the U.S.. Therefore, I would also like to know which American states still have a noncommercial easement in gross which is assignable, based on past precedent i.e. states which have not yet integrated Restatement (First's) in that respect (i.e. in so many words still have profits à prendre independent of the modern easement).
1 I'm revisiting a civil law decision through the eyes of the common law. The landmark decision is The Matamajaw Salmon Club v. Duchaine, since deceased,  UKPC 94,  2 AC 426, with the opinion delivered by Viscount Haldane for the Judicial Committee of the Privy Council, at that time the court of last resort for the Empire, overturning a decision from the Supreme Court of Canada,  S.C.R. 223, on appeal from 27 Que. K.B. 196, concerning fishing rights bought by a famous Canadian character, Lord Mount Stephen, Bt., GCVO. What happened is that in the first instances of the case, reference was made by the Quebec justices to the common law concept of profits-à-prendre. So what you end up having is a very intricate discussion about the foundations of property law and implicit comparisons between the civil and common law traditions. Perusing this material is not required in order to provide an answer.
2 It is not clear whether the economic balance in the exchange plays a role in qualifying of the right someone like (B) would hold. One justice explains Viscount Haldane's inclination to see more than a personal right arising from the fishing right in the aforementioned case, is a consideration motivated analysis of the exchange. The right was granted in exchange of what is assumed to be valuable land, so it must be worth more than some trinket, and therefore justifies a self-contained title of some similar value. (Mc Whirter c. Cochrane, 2008 QCCS 5643, par. 17). For further background on personal servitudes and the impact of Matamajaw on Quebec civil law, see also Club Appalaches c. P.-G. Québec, Laberge c. Émond 2010 QCCS 263, Landry c. 9160-9388 Québec inc. 2012 QCCS 5558, Charbonneau c. Moreau 2014 QCCA 1425, and Fournier c. Lamonde and "Une relecture de l'arrêt Matamajaw", Sylvio Normand, Les Cahiers de droit, vol. 29, n° 3, 1988, arguing Lord Haldane concurred with the Court of the King's Bench of Quebec because he misconstrued its reasons.
3 I wonder on what physical substrate would such a fee rest (if the fee simple requires that - I'm asking); and does one distinguish between fruits/crops and fish (a living being traveling in the river, not constrained to a fraction of it, and not growing out of it) in the profits-a-prendre context at common law? From my perspective, the fish in the river is closer conceptually to that very water, than it is to crops and fruits. It is res nullius, the thing nobody owns, and as such it is appropriation i.e. fishing, which creates property; it is not property before that, that I know of. So can a fee simple be based on that? Plus I read that in UK common law, a profit a prendre, as opposed to an easement, can only be registered if it's in respect of something which can be owned (I quote: eg a right to take water from a spring or pump, or the right to water cattle at a pond may be an easement but cannot be a profit a prendre. Water, when taken, is not owned by anyone; nor is it part of the soil).